Ashita no Nadja has Black Rose (aka Keith Harcourt), a thief who mind-breaks the nobles he steals from and teases Nadja for a lot of things, such as stealing her first kiss. But as it turns out, he is Just Like Robin Hood, and is acting on the wishes of his dear, dead mother.
Jean begins the series as a selfish Jerkass who cares only about getting himself into the Military Police. After the death of his best friend in the battle that nearly destroyed his hometown, he abandons his selfish ways to join the Survey Corps. Emphasized when he comforts Armin after their captor molested him when he was dressed as Historia.
Many characters in Axis Powers Hetalia act like this at some point or another, being jerks to each other during conflicts but genuinely showing kindness and concern for younger nations, animals or their subordinates: America, England, France, Germany, Austria, Prussia...
Kagura from Azumanga Daioh, she is hyper-competitive and barely takes her studies seriously, yet she once helped a foreigner with his luggage, has helped against cats that frequently bite Sakaki, and even when she acts like a full-up jerk, she never means any harm. Tomo and Yukari also qualify; in their case, the "jerk" part is much more apparent due to how they (sometimes deliberately) act as jerks, but their hearts of gold are still there.
Guts is violent, cruel, cold, and obsessed with his personal goals, which are often achieved at great cost or risk to others. But he genuinely cares about the people around him, is a compassionate leader, and his distant, uncaring demeanor seems to come from a desire to keep people away from the danger he's constantly in. It ... doesn't always work out that way.
Serpico is extremely cold, and mainly concerned with Farnese, but because of it, won't complain when occasionally being heroic.
Byakuya Kuchiki is shown to be arrogant and very snobby (possibly to do with his noble family upbringing), but he has been proven on more than one occasion to be fiercely devoted to his sister, Rukia.
Same goes for his lieutenant, Renji Abarai, who is very Hot-Blooded and loyal to those he cares for, including Rukia.
Kensei Muguruma, and his lieutenant Mashiro, get along like an ice cube and the sun, but when the Wonderweiss started beating the shit out of her, the first thing Kensei did was go and save her, then deny that was his intention. He also saved Hisagi from a Hollow when he was young and tried to get him to smile, although he did it in a hilariously frightening manner.
Domyoji Tsukasa of Boys over Flowers, who manages to be a sympathetic male lead despite frequently beating up random bystanders.
Dola from Castle in the Sky. She's a crusty, tough-talking old lady who is abrasive, bossy, and even controlling of her boys. She even tries to kidnap Sheeta (and steal her crystal) at the beginning of the movie. Later on, she grudgingly agrees to let Pazu help her save Sheeta and agree to take them aboard her ship. (While she's playing chess with her husband, who questions her about her affections for the kids, her response is, "Whaddaya mean by that, ya old fool?! I'm after treasure. That's all." Deep down, however, she's actually a softhearted person who comes to admire Pazu and Sheeta for their loyalty toward each other. (She does a brief double-take, though, when she overhears Pazu telling Sheeta that Dola is "much nicer than she pretends to be.")
Muta from The Cat Returns is literally called a Jerk with a Heart of Gold at one point. He fits the build exactly. He has to be coaxed into helping others for selfish reasons, but for friends he's willing to fight an entire kingdom.
In A Certain Magical Index, Accelerator and Stiyl were both introduced (and still are) as totally heartless characters, but were shown to have a heart of gold whenever it comes to their loved ones (Last Order and Index respectively).
Tomoya Okazaki from CLANNAD, who tries to project the image of a wangsty, cynical lazy ass, delights in twisting the truth for practical jokes on anyone and everyone (leading to some impressive amounts of confusion and misunderstanding among the more naive cast — Nagisa especially), and tries to look all bored and detached. Yet he ends up trying to help the main characters of every arc, without a second thought, and has been seen to cry at the ends of some of the arcs, in Manly Tears, or open frustration and sadness.
Lorenzo constantly torments Ian, treats Marjorie like a child, and cheats on Claire with Pascal. Despite this, he has some redeeming moments. He comforts Nadia when Ian falls for Jeremy, even attempting to confront Ian about it. He tries to convince Claire that Marjorie should be given more freedom, and also rescues Jeremy from Pascal's drug-induced abuse.
Ian also fits, by caring about Jeremy, but often gets too angered by Jeremy’s failures, and his attempts to help are… off.
Kurosaki/Daisy from Dengeki Daisy qualifies by being rude and obnoxious in-person. But over the phone... incredibly charming.
Cross Marian of D.Gray-Man fits. He has shown he has his Jerk Ass moments. But, he's not a complete jerkass. The manga has shown many hints and instances to illustrate that Cross isn't heartless, and while many people aren't fond of him, there's many people who apparently think very highly of him. Allen says he lives off lovers and acquaintances. So he's apparently someone you could be fond of, and even want to help, should he care to show his kinder side. He's shown protectiveness, empathy, sadness, concern, and hesitation. Although, most of these things are shown when it comes to Allen and women. He could very well be a victim of Jerk Ass Facade.
On a much smaller scale, Yajirobe. A belligerent glutton who’s been around since Dragon Ball, and who loudly declares he wants nothing to do with the other Z-Warriors, still always ends up coming to their aid when they really need it.
Vegeta himself becomes one in the Time Skip following the Cell Games, where he becomes a loving, if not distant, father to main timeline Trunks, and he's become more attached to Bulma. He also performs a selfless Heroic Sacrifice on Majin Buu later onward, and fights with Goku on friendly terms for the first time against Kid Buu, also fighting for the Earth for the first time. At the end, he's a stark contrast to the callous, self-absorbed Jerkass that came to destroy Earth years ago. This is best shown in Battle Of Gods, where he swallows his pride and tries to please Beerus, and absolutely loses it when he slaps Bulma.
Rouce, a.k.a. Red Lightning a.k.a. Mink's father in Dragon Half. A once-renowned warrior whose recent "exploits" consist of fighting his dragon wife, hitting on any attractive woman (regardless of her availability), faking life-threatening diseases to get out of hunting for food, and pulling down his own daughter's pants, it seems the only thing he's good at now is lying. However, he does get a moment of off-panel awesomeness by singlehandedly slaughtering a horde of monsters about to eat his wife and daughter. Though he appears to be sleeping when the two return to camp, the blood on his sword (and trademark "R" cut on the monsters' corpses) make it pretty clear that he's the one who saved them.
Shizuo Heiwajima from Durarara!! acts like a complete Jerk Ass at some points, but it turns out that, when you don't activate his Hair-Trigger Temper, he's actually just a socially inept sweetheart. He deeply cares about his brother and basically anybody who isn't Izaya Orihara.
Youichi Hiruma never refers to anyone by their real name, only by his personal nickname, and all his personal nicknames start with "fucking" (toned down to "damn" in Viz's translation of the manga). (Sena is "Fucking Shrimp", Mamori is "Fucking Manager", and then there's his best friend Kurita, "Fucking Fatass", and so on.) He's a violent gun nut who slings a constant string of verbal and physical abuse on his team, uses blackmail to get his way like some people say "please", and lies like it was going out of style. He also never fails to reward perseverance, dedication, and effort as long as the team doesn't suffer for it, has his own unique brand of showing affection which he doles out with regularity, and puts himself through all the same crap thatworse crap than he puts everyone else through.
One notable scene was when an exhausted Yukimitsu made it to the top of the Tokyo Tower, as part of Hiruma's tournament to get more teammates. However, Yukimitsu's bag of ice, that he was suppose to bring up to the tower, had all melted. But secretly, Hiruma slipped in an ice cube and congratulated him for making it.
Another example is when an enraged Gaoh was rampaging in the stands looking for someone who insulted someone he considered a Worthy Opponent, Hiruma jumped in front of Mamori and Suzuna to protect them from harm.
Agon at the end, reveals a kind heart by shaving his head to give Unsui inspiration to play for himself. This, after dozens of chapters acting as a bully to everyone.
Linebacker Habishira. Mostly out of blackmail, but even after being released by Hiruma so they can practice, they still help Deimon out a lot.
Marco. All he wanted to do was win the Christmas Bowl for his girlfriend, Maria, and show her the rising sun after the victory, but lost sight when Maria disproved of using Gaou as a weapon.
In Freezing, the third years may be major, major jerks who were obsessed with beating the crap out of the main character for unjustified reasons, but they're still soldiers trained to save humanity from Eldritch Abominations. During the Academy Siege, they were in the front lines covering for everybody else.
Kyou Sohma from Fruits Basket. Despite being a jerk to everyone, he develops great affection for Tohru, whom he eventually falls in love with.. He hates Yuki, but he does seem concerned when the latter collapses because on an asthma attack. Also, he clearly cares for Kagura despite her Tsundere/Yandere tendencies towards him.
Edward Elric acts like a jerk to many characters - including his younger brother Alphonse, who constantly has to apologize for him in the trend of "Don't take it personally, he's like that with everybody."
Greed, who is named after the sin of avarice, isn’t as selfish and insensitive as he claims to be, or as his name would imply. He genuinely cares for the objects and people he “owns”, and is occasionally quite serviceable.
Roy Mustang frequently appears callous and arrogant to those (Ed in particular) who don't understand his past and/or motives.
Takuto, the male protagonist of Full Moon o Sagashite, is snarky, anti-social, occasionally rude ("baka" is his favorite word), he will always say the exact opposite of how he truly feels… Yet when nobody's looking, he'll do something incredibly sweet. Just make sure you don't blink, because you'll miss it. By the end of the anime series, his jerkish side pretty much vanishes. His last action is to sacrifice his life and soul to save Mitsuki from her cancer. A heart of gold as well as it can be defined, indeed!
Naoki Shinjyo started out as a Jerkass when he lashes out at his team's mechanics and gets angry over his poor driving skills despite being The Ace, but once Miki Jounouchi blames him for having no respect towards mechanics and he proves himself as a true racer, he begins to show more of his softer side.
Karl Lichter von Randoll also started out as a arrogant racer when he puts down other racers, saying that he's better than anyone, but after the race with Hayato in the Spanish race that ended in his defeat, he slowly softens up and begins to have a sense of chivalry.
The Fallen Angel and main protagonist of Gabriel DropOut, Gabriel is for the most part an apathetic and rude Gamer Chick, who disregards the very values she used to live by. Even still, she does occasionally have a few redeeming moments:
While Gab herself won't admit it, Vigne acknowledges that she does have a caring side to her, stopping by Vigne's house during one of her sick days to not only check up on her, but to deliver her homework and refreshments which Gab purchased with what little remaining money she had.
In episode 11 she helps Satania keep the dog she rescued by begging the owner of Satania's building to allow pets and even agreeing to work an extra day at the coffee house, all without telling anyone.
While she still loses an awful lot of time, money and effort on her MMORPG, it's fair to say that she is still a healer type in-game, like when she began playing in the first place when she had the best intentions.
In the second OVA, she breaks the rules to give a critically injured blind girl her sight back.
There's also Satania, a boisterous and petty demon girl who adopts the stray dog that keeps stealing his melon bread because she cannot abide for it to be put down at a dog pound. She even gives the dog the bigger half of her melon bread when they reach Hokkaido. Even Gabriel is moved by the gesture and even pulls some strings behind Satania's back for her to be able keep the dog.
In Gakuen Babysitters, Chairman Morinomiya, despite coming off as a cold, old woman most of the time, has shown many instances to be very kind and caring toward her adoptive grandchildren. Even during times where she would vent her busy schedule, after receiving an invite from Kotarou for a play she immediately had things rescheduled so she could attend.
Azusa Mizutani from Gakuen Ouji. The guy is pretty much a dick, especially towards Okitsu, often insulting or igoring her. He also doesn't understand when he's being tactless and hurting her feelings. He does often try to make up for it when he realizes, such as standing up for her and coming to her aid when she needs him. Unfortunately, he tends to go back to being a dick again a few chapters later.
Midou Ban in Get Backers has a mocking nickname for nearly everyone (monkey trainer, thread spool, computer boy, etc.), is selfish, sneaky, gropes women constantly, and is generally just not a nice guy to be around... unless your name is Ginji, and you get to see that "Ban-chan" is really just a cuddly, misunderstood dork.
Gintoki Sakata is rude and snarky to almost everyone and often scoffs off other people's problems as none of his business. However, when push comes to shove, his kindness and sense of honor pushes him beyond humanly possible limits and the juxtaposition certainly makes him seem that much more awesome. Even more, he might risk his own life in order to help the needed ones.
Hijikata from the Shinsengumi is even harsher than Gintoki, but if the situation is very serious, he'll do whatever he can to help those in need of assistance.
Chiharu Eniwa of manga series Girl Got Game argues, shouts, and fights at Kyo almost as soon as he meets "him". Chiharu does have a short temper, but he's actually nicer than he lets on. When he does help someone (usually Kyo), he'll often say "I'm only helping so you don't get mad at me later," or some other half-hearted excuse.
Shin Asuka initially seems to be a troubled youth with authority problems and chews out anyone who tries to help him in most ways, and as the series goes on, it becomes more and more obvious that he is a genuinely nice person. He’s even willing to take care of the enemy Gundam pilot, Stella.
Yzak Joule, after some well-deserved character development: aggressive, stand-offish and generally a Jerkass, he expresses care for Athrun when he's reassigned ("Don't get killed until then..."), and although he's still pretty aggressive by the time SEED Destiny rolls around, he's covertly working for Lacus.
Kamille Bidan is in possession of hugeWangst and can be a big Mood-Swinger, but he also genuinely cares for those he loves and tries to help them.
His rival, Jerid Messa, is more brutal. Basically, he's a huge Jerk Ass, but if you do manage to make him care for you, he'll genuinely do so... before you eventually suffer the Cartwright Curse.
Mobile Suit Gundam AGE: Woolf in the first generation. He enjoys annoying his crewmates and tries to nab the Gundam from Flit, but he looks out for Flit in combat. By Gen 2 he's still a cocky maverick, but much more of a mentor figure.
Van of GUN×SWORD will dismiss someone’s plea to rescue their town because it has "nothing to do with" him, but then he'll think better of it, especially after his Morality Pet Wendy prompts him a little (or gives him an outright scolding). Speaking of Wendy, he takes her for granted much of the time and occasionally treats her rudely, but if she's sick, in danger, or even just unhappy, he acts surprisingly tender towards her.
Mamoru Takamura only cares about boxing, and therefore takes it very seriously if a boxer disgraces himself, and he respects a boxer that fights well, regardless of the results of the fight. Aoki and Kimura get especially surprised of him when he approaches Ippo, not to mock him, but to congratulate him after he loses against Date Eiji. He was also extremely brokenhearted after the “Bear” incident. Because Nekota had killed the very same bear that he had spared on account of her caring for her cubs, he literally cries. For a guy that beats up his fans and grabs people's cocks in the shower on a regular basis, this shows that he at least has some kind of idea of common sense.
Also Takeshi Sendoh, who is Hot-Blooded and a borderline Blood Knight... but actually started fighting to protect people rather than hurting them in purpose.
Hanaukyō Maid Tai. Konoe, especially in La Verite. She starts off very stern and strict with Taro, but ends up becoming friendly toward him
The titular character is selfish, bossy and arrogant, but she does treat the Brigade members very well, like after Kyon fell into a coma in Disappearance and when Yuki fell sick because of the Sky Canopy Dominon in “Snow Mountain Syndrome”. Most recently seen in the end of the beta storyline of Dissociation.
Kyon is prone to presenting himself as a world-weary Deadpan Snarker, but he's a deeply compassionate person who treats everyone equally and seriously in thought, if not in action.
InuYasha has the titular half-demon, who is frequently abusive to his companions, physically and verbally. When Kagome describes his behavior to her friends in the modern world, they all consider him a Juvenile Delinquent. Despite this, he is very protective of his True Companions, and trying to hide his feelings of love for Kikyo and Kagome.
Jin has Nokaze and Tanosuke, both of whom come across as rather jerkish in their first appearances. As they and Jin get to know each other better, they slowly reveal their hearts of gold - Nokaze collects money to pay for treatment of her co-workers and Tanosuke buys Jin's debt when the doctor has to lend money to save a courtesan Tanosuke has made pregnant.
Joseph Joestar, as he appears in Battle Tendency, is a short-tempered youth who is prone to picking fights, but he cares deeply for his grandmother, such that when he was caught up in a mid-air hijacking as a child, he brutalized his assailants not because they hit him, but because their hitting him caused him to accidentally stain the sweater his grandma gave him with blood. He also goes out of his way in his first appearance to help a kid who picked his pocket when he gets jumped by a pair of crooked cops.
Jotaro Kujo, from Stardust Crusaders, is not a very nice man by his own admission: he starts fights at school with students and teachers, considers female students fawning over him a pain in the ass, skips the bill at restaurants if he dislikes their food, and gets annoyed by his mother's doting nature. Nonetheless, he is not only fiercely loyal and protective of his friends, but is willing to travel halfway across the world to save his mother from DIO's curse.
Layla Hamilton from Kaleido Star, the Broken Bird who is as tough on herself as she is on new recruits to the Kaleido stage, and has quite the daddy issues.
Tomoe from Kamisama Kiss is normally sarcastic, rude and highly critical of just about anything Nanami does. But if anybody else tries to insult her and/or criticize her, he is quick to come to her defense. If you hurt or threaten Nanami in any way, shape, or form, you're in for a world of pain.
Gareki, who is Tsundere, still has a weak spot for Nai’s innocence (though it won't spare the poor kid getting bonked in the head, and all the other annoying brats in the world can go rot for all he cares).
Hirato seems to effectively hide how much he cares for his crew and how often he makes certain of Nai's safety.
Akari is harshly vocal about Hirato's apparent callousness toward his crew and the people essentially under his care, before turning around and doing essentially the same thing.
Tanimoto acts like a Jerk Ass towards Kenichi, but when push comes to shove, he's willing to throw his lot in with the Shipaku Alliance.
Nijima seemingly doesn't care about the desires or well-being of the Shinpaku Alliance (especially Kenichi), but he has shown that his is willing to stick out his own neck for the team when he really needs to.
Akira Hongo, the "God Fist" of YAMI's One Shadow Nine Fists, looks and acts like a very aloof fighter, but over time he is revealed to have been a very good mentor to his now-deceased prize student Sho Kanou (and later, to Kanou's fellow students under him as well), and he didn't take it very well when he learned that Kanou had died at the end of the D of D Tournament arc. It's also indicated that he's always respected the bond between master and student (hence the reason he advises Sakaki to go support Kenichi instead of fighting the Demon Fist, which he does himself) and Kenichi earns his respect for standing up for Kanou's self-sacrifice to protect Miu during the aforementioned D of D.
Ryuko Matoi from Kill la Kill is short-tempered, foul-mouthed, and is 99% of the time driven solely by revenge. Beneath her rough exterior, however, is a kindhearted girl who cares deeply for her loved ones and is willing to help anyone in trouble, just as long as they don't try to get eye candy from her, and when she's given the chance to kill the two people who caused her the most misery, she decides to forgive them.
While Pauley Cracker from Kimba the White Lion can be sarcastic and pushy, he cares deeply for his friends and is willing to do whatever it takes to help them.
Kimi ni Todoke presents Pin, the apathetic homeroom teacher, who shows little to no sympathy for any of his pupils, goes out of his way to embarrass people and generally just acts really rudely to just about everyone. Despite this, though, his Pet the Dog moments and occasions on which he actually gave pretty good advice have shown that he's not so bad, deep down.
The Shinka, in the anime for Love, Chunibyo & Other Delusions, is always abrasive towards everyone else in the club. However, the fact that she joined their beach vacation is a telltale sign that she's far friendlier to them than she'd ever like to admit. Her heart of gold is especially highlighted in Episode 9, when she actually gives Rikka advice on romance.
Vita from Lyrical Nanoha. She has something of a fiery temper and is rude to everyone but Hayate. At the same time, she's violently protective of those she cares about (which, by the time of StrikerS, is pretty much the entire main cast). Although the jerk part faded as the series went on.
Alto Saotome from Macross Frontier acts like a jerk to a lot of people and (in the beginning) mutters about how much he hates his home, Frontier, but in spite of it does everything he can to protect it. The Belligerent Sexual Tension between him and (Tsundere) Sheryl leads to the obvious conclusion.
Chamo, the Weasel Mascot, is a Dirty Old Man in ermine form, and constantly tries to manipulate people for his own gain... but he never puts his own goals above the safety of the rest of group, tries to make sure everybody else benefits along with him, and generally tries to make himself as useful as possible, even when an ermine generally wouldn't be able to do anything.
Ayaka Yukihiro has her moments of charm as well — when she's not being a Rich Bitch and Ojou — she shows herself to have strong principles and be genuinely quite caring of others.
Tosaka constantly bullies Ako, and constantly complains about her, Negi, and everyone else. He willingly turns over the evidence that could send Negi to prison at no cost after blackmailing him with it, even though Ako volunteered all of her rights and was willing to essentially become his slave for life. Tosaka implies that while that is what she might have meant, some rather nastier things may have happened as well if she'd gone through with it. However, he also tells Negi that his Missing Mom, Arika, was an extraordinary person, and he cherishes the memory of the single time he met her (when Tosaka was a mere Street Urchin) very fondly. And later, he chooses to make a Heroic Sacrifice, Taking the Bulletfor Ako.
Dynamis seemed to be an Aloof Big Brother/villain, who is completely condescending to Fate’s Quirky Miniboss Squad, saying what a shame it is that Cosmo Entelecheia has gone from being a massive organization to relying on four little girls to do their dirty work. Then he thanks those same minions for staying with the organization, because without them it would have been impossible for them to have gotten as far as they have, and that they should be proud of themselves for surpassing the Cosmo Entelecheia of the past. Koyomi even lampshades Dynamis’s surprisingly caring speech.
Chisame, being the Only Sane Woman in her class, remains pretty snide and sarcastic as she gets drawn into Negi's magical adventures. However, she repeatedly demonstrates that she cares deeply for him and her classmates, and wants to be off adventuring with them, despite her protests to the contrary.
While Evangeline for the most part insists on playing Token Evil Teammate to Negi and the gang, she is constantly giving them advice and has rescued them from life-threatening situations on more than one occasion.
Himari's possessor, in Mawaru-Penguindrum, is an entity that horribly insults a young girl like Ringo all over when summoning her a Shoma to her presence, and some episodes later summons both of them again... to give a Ringo, who has just had a Heroic B.S.O.D., some space to cry about her huge troubles. During which, it is still calling her mean names.
Couch Mountain seems like a cruel man who makes students run laps for no reason, and seems to be doing deals with shady characters. In reality, he was trying to buy land to put up a park for poor children. And then, in the end, he makes the main characters run some more laps for staying up late.
Lead bully Samatha might also be one of these, charitably keeping around her totally incompetent minion Spyke and often helping the heroes out when they really need it. She just does a damn good job at hiding it (and does actually fire Spyke in one episode, though not without provocation).
Hitoyoshi Zenkichi from Medaka Box definitely qualifies, he moans about having to do things all the time, will chew someone out in a moments notice, gives up constantly and he goes to extreme lengths to show how awesome he is (in one week he tried out every club the school had to offer earning the nickname Bukatsu Storm), but if you even think about doing something to one of his friends he will make sure you go down, even if he has to go down with you.
Taishou from Mekko Rarekko is a great example. At first, Taishou was a bit of a bully and a Jerkass towards Buchi his only friend in the first two volumes. But the reason that the two are friends is because back in second grade when Taishou saw that Buchi was being bullied, he wanted to help him out. And its not just because he felt it was the right thing to do. Taishou was bullied a lot in first grade. One could even call it torture and when he saw that Buchi was being bullied, it reminded him of his Dark and Troubled Past and he didn't want to see someone else go through the pain of being bullied.
As noted above, Taishou still isn't the greatest person in the beginning of the series. Because he grew jealous of Buchi working on a project with Fukami, instead of with him he ends up raping Buchi. After a punch to the face from Fukami, he realized what he had just done and he breaks down in tears. He gets much better in the third issue after he takes a level in kindness and he goes from a Jerkass to a Jerk with a Heart of Gold.
Les Misérables: Shōjo Cosette has Eponine as an adult. She is still mean as an adult, but she is much more troubled by her actions, outright hinders her father's criminal attempts when she is not avoiding associating with them, and generally comes as sympathetic and regretful of her mistreatment from... everyone she wronged.
Mitsuba from Mitsudomoe has a dismissive and superior attitude towards everybody. Yet, she just as often slips up and reveals that there's some genuine kindness in her. One of her earliest examples is the replacement pencil cases Futaba made. Mitsuba kept using hers well after her sisters no longer were.
While Toru Muhyo is typically fairly cold, showing either irritation with or disdain for those around him, he often does this to teach Roji subtle lessons, and typically goes out of his way to get the best possible result for the ghosts he deals with, even when he seems to be taking a harsh stance on them.
Rival Executor Daranimaru Goryo may appear a ruthless bastard, but he actually shows genuine concern for his assistant Ebisu, and even cries over him. Twice.
Murasakiiro no Qualia: Tenjou acts like a jerk towards Yukari but has actually always been doing her best to try to understand her better. This attitude only manifested after the event in their past.
Nadia herself wavers between being a complete Jerk Ass and a Not Good with People sort of person, but in the canonical episodes of the story, she fits into this trope. Aside from being suspicious of other people, she has a nasty, quick temper and gets angry quite easily, misunderstanding everyone's actions at the drop of a hat. That said, she is also shown growing to care for Jean, as evidenced by her attempt to comfort him about his father's death, and even suggesting him to build another aircraft to cheer him up. She even brings him a half-baked dish of seaweed. She's also transformed by the end of the show into a genuinely caring person. She sacrifices her Blue Water's power to resurrect Jean, and even marries him.
Captain Nemo is very reserved most of the time, and sometimes makes harsh decisions. However, he’s fundamentally a good person who cares for his crew and mainly wants to stop Gargoyle from destroying the world. He even comes to see Jean as a surrogate son and has a soft spot for Nadia. It turns out he's her father.
In Part I, the eponymous character (Naruto Uzamaki) was a brash, temperamental brat fond of picking fights with everyone and completely lacking in social graces, but he was also surprisingly kind to people like Inari and one of the few to interact with Gaara as an equal rather than with fear or hate. During ‘’Shippuden’’, his childish behaviour is downplayed, as he matured both emotionally and physically over the Time Skip. Justified in that he was a pariah of sorts because of him being the jinchuuriki. He was ostracized and thus developed as he did. When people actually showed kindness to him, we get to see that he cares deeply for his friends and loved ones.
Sasuke Uchiha, on the other hand, is a complicated issue. He fed a tied-up Naruto during the bell exam, in violation of the test instructions. The scene where he saved Naruto's life and told Naruto that it was his duty to save Sakura, where he said he didn't want to lose those important to him doesn't leave any opening for interpretation. He was a Jerk with a Heart of Gold... sadly, the emphasis is on was. Although since the second stage of the Fourth Shinobi War, he may be turning good again, because he chose to protect the Hidden Leaf Village rather than destroy it.
Sai is introduced as an abrasive Jerk Ass, but mellows out while Naruto establishes bonds of friendship and camaraderie with him. He tends to make insulting comments from time to time, but typically in misguided attempts to become friends with Naruto and Sakura.
Neon Genesis Evangelion: Asuka Langley Soryu is an angry and temperamental Tsundere, but despite that, she still tries to be compassionate to Shinji; this even more visible in the manga version, post her initial appearance in Volume 4. Unfortunately, he's just too secluded to open up to her, leading to many angry confrontations between the two over his cowardice and her arrogance.
Magari Kazuma of Nora spends the first two volumes of the series treating the titular Hot-Blooded demon like a misbehaving puppy and most of his classmates like idiots, claiming flatly to make decisions based solely on which outcome will most benefit or least inconvenience him, and being generally bastardly to everyone. And yet... he will do anything to protect the people around him, often foregoing magic and just leaping irrationally to their defense, quite at odds with his normal Magnificent Bastard-in-training persona. And you really don't want to imply that humans are inferior; the results are not pretty.
Nezumi from No. 6 is nasty to most people, and violent at the very least provocation. But he also sings to Dogkeeper's dying pack members to ease their suffering, to say nothing of what he'll do where Shion is concerned.
Haru Jigokumeguri from Ojojojo is a unique case in that the jerk part is actually subconscious due to a bad case of Becoming the Mask. While she is a genuinely sweet girl, she often finds herself slipping into her Rich Bitch persona and acting condescending to those around her, including her friends and boyfriend (though she gets better as the story progresses).
Roronoa Zoro acts distant and somewhat insensitive to others, but has shown himself willing to go through Hell and high water for his True Companions. Most of his Pet the Dog moments deal with Morality Pet, Chopper.
Nami, who is The Scrooge, is also hiding a heart of gold. She was introduced as a thieving jerk. It seemed a Jerkass Façade in order to help her village from a ruthless gang lord, but after she was freed from her debt, she made it apparent that she was still as greedy and manipulative as ever…which is justified to an extent, due to the fact that her family was very poor before her village was taken over. She has shown a soft spot for women and children and, thanks to Character Development, even was willing to give up part of her wealth to Rolling Lola out of thanks. She eventually is able to forgave a former member of the gang that had terrorized her village and tried to help him win back a kidnapped mermaid friend with a large part of the wealth collected by the crew.
Smoker revealed his heart of gold in one brief scene. A little girl with a 3-layer ice-cream cone bumps into him, and instead of getting pissed at her for staining his suit, he gives her money to buy a 5-layer ice-cream cone, and apologizes to her.
Curly Dadan is Luffy and Ace's foster mother. She isn’t very kind towards her young men, constantly complaining about how much of a nuisance they are, and can’t even praise without calling them “idiots” or “assholes”. Despite this, she is very protective of them.
Pekoms of the Big Mom Pirates comes across as very abrasive yet when he saw that the Strawhats saved his family and home he broke down in tears of joy and thanked them on his hands and knees. He was also go to lie to Big Mom's face that he did not see them; if only Capone wasn't there also.
Besides her villainy, Jessie of Team Rocket really is a jerk: she has a harsh personality, a leadership style that ranges from "despot" to "tyrant", and is self-centred to boot. Despite this, she cares deeply for her friends and her Pokémon and has several times sacrificed her own happiness on their behalf. (See Chansey, Dustox, every Team Rocket Breakup Episode ever.)
Pokémon Special: Black is introduced with Jerkass attitudes, (see his treatment of Bianca during the first gym battle), but after he's been called out on this, he has made an effort to stop acting like a Jerk to people.
Randou, from Pretty Face, went to such an extreme in Jerk Ass behaviour that basically everyone he was in contact with either fear or hate him. The only exception to that is his crush, Kurimi, who sees the heart of gold within him. Eventually the gold part becomes more noticeable.
The Prince of Tennis: Kaoru Kaidoh, master of “The Snake” (In professional circuits, the Buggy Whip Shot), enjoys acting like an aggressive cobra around other players. Cold stares, heavy breathing, and frightening glares. All of this is hiding his heart of gold; in the anime, he nearly drowns trying to save a puppy.
Fakir, the jerkish, controlling guardian of Mytho in Princess Tutu, who turns out to be using the tough exterior to hide his fear of being killed in service as Mytho's "Knight" and being a failure in the end.
Kyoko from Puella Magi Madoka Magica. She's very callous and selfish, advocating that magical girls should only use their powers for their own benefit. In her first appearance she would have killed Sayaka if Homura hadn't intervened, but after learning the Awful Truth that magical girls are basically liches, she becomes much less antagonistic. Her heartbreaking backstory makes it clear that when she says magical girls should be selfish, she really is trying to help Sayaka by preventing her from making the same mistakes she did. Her shift away from jerkassitude is made clear when she saves Sayaka from Homura, in an ironic reversal of their first encounter. Her heart of gold becomes especially apparent after Sayaka becomes a witch and she tries to bring her back. This fails, and Kyoko uses a suicide attack on Sayaka so that she won't have to die alone.
Ranma ½: While Genma Saotome may be selfish and abusive towards Ranma, he still cares about his son. In a Crowning Moment of Heartwarming, he gives a young Ranma his blanket when both are cold.
Gin slowly develops from a Handsome Lech who describes all of his relationships as “conquests” into one of these. It begins with him taking the blame for causing problems on campus although it was actually one of his ex-girlfriends who was at fault, as well as becoming a One-Man Army against the Fairy Tale organization because they were messing around with his friends, specifically Sun, the one girl who has gone toe-to-toe with him and gained his respect.
Inner Moka as well, first introduced as cold and uncaring towards everyone around her. As the series goes on, she starts to become more appreciative towards her friends, and eventually falls in love with Tsukune by the end of the manga.
Mamoru Chiba/Tuxedo Mask, the title character's love interest, starts out as a Deadpan Snarker "snob" who enjoys teasing Usagi about everything. Even after he’s revealed to be the Tuxedo Kamen/Mask that’s been rescuing the girls, he insists on Malicious Misnaming Usagi as Dumpling/Bun-head (“Meatball Head” in the anime's DiC dub.
Rei Hino/Sailor Mars is impatient, cocky, and easily the most critical of Usagi out of the Inner Senshi. A few times, Rei had even goaded other Senshi into mistreating Usagi as well. Rei also made a little girl cry in the SuperS season. Yet she is staunchly loyal to Sailor Moon, comforting Usagi when she is in true distress, gave her life to keep Sailor Moon safe twice, and stands up for Sailor Moon when the Starlights berate her. She is also protective and encouraging towards Ami Mizuno/Sailor Mercury.
Makoto Kino/Sailor Jupiter, is a Subverted example. She is assumed to be a violent bully because of her temper, but she's actually very sweet after becoming friends with Usagi, and is one of the most patient and motherly of the Inner Senshi.
ChibiUsa spent a good part of the R season antagonizing Usagi, even though Usagi saved ChibiUsa's life as Sailor Moon many times, often getting seriously hurt in the process. Even after ChibiUsa learned that Usagi was Sailor Moon, she still had such a low opinion of Usagi that she couldn't bring herself to respect Usagi as Sailor Moon, and stole Usagi's Silver Crystal brooch, which eventually led to Rubeus kidnapping the Senshi. Nevertheless, she grows to appreciate and admire Sailor Moon (though she never misses an opportunity to insult her) and the rest of the Senshi with time. ChibiUsa also develops a heartwarming friendship with Hotaru/Sailor Saturn, and would give her life to protect her.
Haruka Tenoh/Sailor Uranus: She may be harsh towards the Inner Senshi, especially Sailor Moon, but after Sailor Moon saves Hotaru from Pharaoh 90 while sacrificing the Holy Grail in the process, and later proves herself against Uranus and Neptune, Haruka finally accepts Usagi's fate as Messianic Archetype.
Minako Aino/Sailor Venus comes off as this to an extent in Codename: Sailor V (less so in the anime). She is brash, fist-happy, and constantly treats Artemis like crap (which genuinely hurts him). But she regularly defends fellow students from bullies, will endure a great amount of hardship in the name of her mission, and would protect Sailor Moon with her life (and expects the other Senshi to do so).
Genjou Sanzo, from Saiyuki, makes (empty death threats) at his companions, calls them his servants, and often employs physical violence on them. BUT, he rescues Goku and keeps the kid around even though there's no advantage in doing so, gives a pep talk veiled in rudeness to Yaone and Dokugakuji during "Against the Stream" so they'd get over their confusion, repeatedly says he won't interfere, won’t help, and is not on anyone's side, but then proceeds to do so, often with an excuse.
Touka Ryuumonbuchi comes off as something of a Rich Bitch who's full of herself. It turns out that her entire reason for recruiting the Ryuumonbuchi team was to create a strong team so that her cousin Koromo, a mahjong prodigy who has been isolated since the deaths of her parents, can face many strong opponents and make friends. Touka also, in spite of her intense but one-sided rivalry, has her butler Hagiyoshi fix Nodoka's stuffed penguin Etopen, partly on Koromo's request.
Hiroe Atago often taunts and insults her opponents, but Hisa, the recipient of such taunts, realizes, while in the midst of a nervousness-triggered Heroic B.S.O.D. that Hiroe wants her to play at her best so she can enjoy herself. Hiroe is also quite nice to her teammates, particularly her younger sister Kinue.
Ban from The Seven Deadly Sins comes up as a jackass who doesn't care about anything but himself and the stuff he steals. His backstory, however, reveals that when he went after the elixir of immortality, Elaine told him that if he were to take the elixir, the forest surrounding it would die. Ban promptly decided that it wasn't worth it (claiming that the wild berries used in one of his favorite drinks was grown in that forest). He may be a thief, but he is not a monster.
Megumi, of Servant × Service, tends to frequently verbally bitchslap everyone, particularly Hasebe and Ichimiya. On the other hand, she's shown to be quite the Cool Big Sis figure for Touko, and generally gives Lucy advice that is actually sound in context. She also goes out of her way to help save Hasebe and Lucy's relationship.
Giroro of Sgt. Frog is normally a hard-boiled warrior, but he's proven that he's willing to go all out to protect the squad. And even moreso, Natsumi. He also shows his softer side to his cat.
Kiyoshiro, from Shattered Angels, begins his characterization by ripping dresses off of female students. His heart of gold is shown when his brother convinces him to change his behaviour.
Yuuki Natsuno, in Shiki, is cold and distant towards others, not to mention he hates the village he lives in, but when a vampire attack occurs he isn't afraid to put his life on the line to stop them.
Zelgadis, especially for the anime, is cold and arrogant, because he just wants to be human again, and he cares for his companions, especially for Princess Amelia. In the original novels, though, he is more of a straight-up Jerk Ass.
The novel-exclusive character Luke has similar justifications to Anime! Zelgadis.
Black*Star often seems so full of himself he hardly has time to care about anyone else, but he does care for his scythe, and is willing to "share the stage" with Tsubaki. While he fights Crona (with brute force, as always), he does attempt to create Defeat Means Friendship by insisting that Crona could have someone to rely on in him, the one around whom the world revolves (or something to that effect). He also goes off to get revenge for Maka while she is recovering from a battle, and flies into a panic when Soul is hospitalized.
Soul is usually the Deadpan Snarker that appears to only really care about advancing himself, but he also cares for Maka, and regularly protects her from harm.
Mifune is one of the best swordsmen in the world and regularly faces off against Black*Star, yet carries around candies for children and swings his sword for a small child witch named Angela.
On the one hand, Stein’s Mad Scientist tendencies (dissecting scythes For Science!) are disturbing when not played for laughs, while on the other hand, it becomes clear over time that he does care about the people around him.
Manabizaki from SWOT is more concerned with studying than with people. He insults people and treats everyone as beneath him since he has "the greatest brain in the universe." Or, at least, he claims not to care. He's come to the rescue of a wimpy male classmate (later a friend) more than once and an ex-delinquent girl he's developed a crush on. His sputtered and obvious excuse? The people attacking them were making too much noise for him to study. Or he was just on the way to a test/class/study-session and the guys were in the way.
Wakatake of Tantei Team KZ Jiken Note is egocentric and has a bad temper. However, it is quite obvious that he doesn't seem to have much evil intentions, has a hart of justice, and will help out his friends when the need arises.
Asada from Team Medical Dragon frequently acts like a misogynistic, perverted, carefree Jerkass. Then a patient gets in with an improbable injury, he saves the day and proceeds to lecture everyone about how the patients' well-being is the most sacred priority.
Nishiki Nishio from Tokyo Ghoul. When first introduced, he's described as having an abrasive personality that makes most people wary of him and repeatedly tries to kill Kaneki over petty misunderstandings. Later on, however, he turns out to be deeply devoted to his human girlfriend and after being hired on at Anteiku, becomes a good friend to both Kaneki and Touka. His voice actor even describes him as a Tsundere, pushing others away out of fear of being betrayed.
Sayaka from Tonari no Kashiwagi-san is a jerk by her own admission, and tries to maintain that perception, but will help out if she can. She even wrote study notes for Yuuto, who she has a notably frosty relationship with.
Nicholas D. Wolfwood, from Trigun, insults you, beats you up out of "affection" and struggles with the Sliding Scale of Idealism vs. Cynicism by sadistically killing bad guys. This is all because he's actually an altruistic and generous dude. The “violent jerk” traits are toned down in the anime, leaving a cocky and pessimistic attitude.
Ataru Moroboshi, of Urusei Yatsura, who combines this with being a Casanova Wannabe. It's strongly hinted that the reason Lum loves him so much is because she can see the noble parts of him that most others (including himself) can't.
Hamel, the titular Violinist of Hameln (manga continuity only). He purposely humiliates people, charges exorbitant prices for anyone who hears his music, plans zany schemes to make money, actually uses his friends as ammunition and is so selfish he'd rather eat his crow companion than go hungry for even a little while. And believe it or not, he really is a good guy underneath it all.
Sawamura Takeshi, in Wa Ga Na Wa Umishi, because the main character Rintarou rubs him the wrong way. He's not above hitting and threatening Rin frequently, but he's also saved Rin's life more than once. Whenever there's a job to be done he's the man to do it. Grumbling all the way.
Tsume always acts tough and cynical, frequently arguing with the other wolves, and doubting their belief in Paradise. Still, he becomes protective of them, especially the younger wolf Toboe, who idolizes him.
The human, Quent. When he's not obsessed with wolf-hunting, he can be a fairly decent guy, if you buy him a drink.
Seto Kaiba is an arrogant male Rich Bitch, who rips up rare cards just so that he can have the only copies in the world. But his asshole attitude is because he’s made himself hard to take care of his younger brother, Mokuba, whom he is fiercely protective of. He actually was a Jerk With A Heart Of Jerk when first introduced (and even tortures Mokuba in the manga after he loses a game), but Dark Yugi's Mind Crush destroyed the evil in his heart, letting him rebuild himself as a Jerk with a Heart of Gold.
Katsuya Jounouchi (Joey) is a juvenile delinquent who used to bully Yugi. He stopped because Yugi was trying to protect him from older bullies. He never forgets this debt, and pushes himself to win the Duelist tournament for his little sister’s eyesight operation.
Hiei is a jerk, long past his initial appearance. His favourite target of mockery is Kuwabara, mostly for his weakness and stupidity. Late in the series it’s revealed that Kuwabara is the only pureblood human in the gang, marking him as exceptionally strong for the category. But his re-introduction as Yusuke’s ally reveals that he’s being driven by the desire to protect his sister. After working together, Hiei also seems to respect his allies, and becomes a loyal companion.
Yusuke Urameshi is a street fighter, juvenile delinquent, and generally has an extremely negative outlook on life. In-series he’s called out on lacking the basic manners of being a human being, but he cannot stand those who hurt the innocent, and is EXTREMELY protective of his friends.
Kazuma Kuwabara is in competition with Yusuke for “The Toughest Juvenile Delinquent” in their entire school. Both are daily brawlers and the lowest scoring students in the entire school. Although Yusuke treats him as an Unknown Rival, the rest of the school is usually just as afraid of either one. But when a teacher threatens to get one of Kuwabara’s gang mates to lose their job, Kuwabara accepts any humiliation, and studies as hard as he can to help his friend. When a demon comes to make Kuwabara commit evil acts, he can’t even steal a comic book properly.
Yanda from Yotsuba&! is an example. He makes himself an enemy of Yotsuba very quickly; he frequently taunts her and makes fun of her, even to the point of making her cry sometimes. Even the adults consider Yanda a fool and usually side with Yotsuba, but it's easy to see Yanda doesn't act out of spite and is a big kid himself. This is most clearly obvious when Yotsuba is sad after her beloved teddy bear is damaged and only Yanda can shake her into action by pestering her. When she begins to sulk after finding out Yanda will go camping with her family and friends, he even lets the other children draw eyes on his eyelids to make her laugh.