Even in his darkest iterations, Batman does what he does so that one day, there'll never be another little boy forced to watch his parents get killed in the street.
Also, Damian Wayne, Batman's son. In Batman #666, as a Future Bad Ass, he is shown having a pet cat he named Alfred. And in canon, he was visibly disgusted and threw up when he saw hundreds of dead bodies of children. Also from canon, he has been visiting Hush (who had surgery to make him look like Bruce Wayne), who was imprisoned in the Wayne Tower, and playing chess with him. Hush suspects that he does this because Damian is grieving for his father and it's a way for him to spend some time with his father.
Jason Todd, despite the things he's done and the murders he's committed, takes in Sasha, a young girl whose face was mutilated by villain Professor Pyg. When she feared that the mask that Pyg had stuck to her face would make it that no doctor could fix it, he assured her that it wouldn't make her any less special. In Red Hood and the Outlaws it's shown that he deeply cares for the All-Caste, considering them his family and hesitating when confronted with their zombie forms, and once saved a village.
Poison Ivy as well. Despite being a fanatical ecoterrorist who gets entertainment out of throwing living people to giant flesh eating plants, she deeply cares about her friend Harley Quinn, and has been a jealously protective and loving Mama Bear to the stray children who fell under her care while Gotham City was ravaged by an earthquake.
Flash Forward, a.k.a. "Negative Man" is an irreverent smartass who never has a nice thing to say about anyone, he has a soft spot for introverted teammate Ava and often seems like the only person who cares about her, and vice versa.
Robotman (though he doesn't technically have a heart: or if he does, it's made of some other metal).
Guy Gardner. Rowdy, egotistical, self-centered, boisterous, loudmouthed, short on impulse control and long on bravado. However, his side of the Slap-Slap-Kiss relationship between him and teammate Ice is genuinely tender and sensitive, a fact that Ice's friend Fire flat out refuses to believe. Additionally, originally he consciously put on his tough guy facade to cope with being The Un-Favorite with an overachieving big brother.
And underneath his bad attitude is a true hero, a man willing to fight and die to protect the universe from harm and deemed best suited to lead the GL Corps as the #1 Lantern.
In his early, pre-Green Lantern days he was a kindergarten teacher. Hal had to save him when he hurt himself rescuing a busload of his students he was taking on a field trip.
The bus rescue happened at the beginning of the issue that introduced John Stewart in 1971, the Jerkass persona came about later with the Crisis on Infinite Earths in 1985. It was apparently attributed to brain damage caused by his many misfortunes in the previous decade or so, starting with the injury he suffered at the aforementioned bus rescue when the bus fell on him and culminating with a few years in a coma before the Guardians revived him.
John Stewart was a bit of a jerk in his first story. He was belligerent enough for Hal Jordan to question the Guardians' judgement about having him recruited as his new backup. However, Stewart quickly proves himself and Jordan happily concedes at the end of the story that while Stewart's outspoken style might be off-putting, he's still an excellent recruit.
Hawk from the Teen Titans, in some writers' interpretations. Otherwise, he's more known for being an outright Jerkass.
Lois Lane is gruff, hard-nosed, sharp-tongued, quick-tempered, bossy, rude, and more than a little bullying; but she's deeply compassionate, has unshakable integrity, is fiercely loyal to her friends and husband, and loves her job because it allows her to help people and fight for truth, justice, and the American Way. And kind, laid-back Clark Kent's attraction to her has strong (though gender-flipped) All Girls Want Bad Boys vibes.
Modernversions of Supergirl tend to put an emphasis on her being a teenager who has seen her family dying and her home exploding before being trapped in a strange (comparatively speaking), primitive world and gifted with powers beyond understanding. So, she's moody, snappy, inmature, rude and short-tempered for a while until she outgrows her loneliness and anger management issues. However, even at her worst she's a good girl deep-down who tries to help people and doesn't want anybody to get hurt.
In the Red Daughter of Krypton storyline her anger was out-of-control and she was abrasive and often plainly rude. Even so, she tried to be considerate to others, apologized when she screwed something up and chided one of her teammates for not being tactful enough.
Elseworld's Finest: Supergirl & Batgirl: It's well-hidden but Batgirl has one. Although Barbara is rude, rules Gotham like a dictator and spends a good while complaining and ranting about metahumans, she doesn't want Kara to kill Lex Luthor - even though she also hates Luthor! - because Supergirl is "a symbol of hope, not revenge".
Superman vs. the Amazing Spider-Man has J J Jameson and Morgan Edge, two curmudgeon, overbearing, obnoxious, borderline-abusive bosses. Amusingly, they are willing to admit their employees' merits when said employees are not around.
Morgan Edge: Kent is my best reporter — or would be, if he were around when I need him! JJJ: Reminds me of a photographer I know — Peter Parker — good, but — er — unreliable!
Perry White is a harsh and short-tempered but fair boss who clearly cares about his employees. In The Phantom Zone, Perry quickly switches from shouting that he will have Charlie Kweskill's head on a platter (if he does not get his assignment done soon) to insist he takes one day off (when Charlie shows signs of being sick).
Lil i Put: The titular characters are both scammers and bums but they more than once proven loyal friends to Miksja and Kirki and are willing to put their own lives at risk to save their friends and protect each other
Shazam! (2012): Billy Batson's kind-heartedness is buried underneath a lot of cynicism. Notably, his first non-selfish act using his powers is defending someone from a mugger.
Wonder Woman (1987): When Artemis was first introduced she cared for the safety of others and was willing to risk her life to protect strangers but was so cruel with her words she drove one man to suicide and told an abuse survivor that her children would be better off if she'd died because she was disgusted the woman was such a "coward" that she took her kids and fled for their lives instead of confronting her abusive husband.
