Heartwarming / Harry Potter and the Nightmares of Futures Past
Harry feeling hope for the first time in years when he discovers a way to travel back in time in Chapter 1. Dumbledore tries to talk him out of this in portrait form.
Dumbledore: Harry, what you're proposing is unbelievably foolhardy. You're going to kill yourself, hope your spirit will physically move through the field, hope the temporal field behaves as you think it will and transports your spirit into the past, and hope that your spirit will be drawn to your body. This isn't a plan, Harry, this is little more than guesswork and good intentions.
Before going back in time, Harry makes sure that the Americans will be able to find Dumbledore's portrait, knowing that Albus would be able to help with advice and knowledge after the war. After everything they been through, Harry forgave Albusfor his manipulations in the past and is treated as an equal by the old man.
When Neville asks Harry if he's alright after a disastrous first potion lesson when Snape deducts 100 points from Gryffindor, Harry instinctively calls him "Nev", a nickname from Future!Harry's timeline when he assures the boy that he's fine.
Molly and Arthur offer to become Harry's legal guardians after Vernon beats him within an inch of his life. Harry is moved to tears by this.
On their way to Hogwarts during Year 2, Ginny encounters some of the Slytherins harassing Luna then gets the others together to save the girl. Mixed with Crowning Moment of Awesome when we see Ginny perform the Bat-Bogey Hex for the first time instead of just hearing about it in the books.
After Percy lectures them about fighting, everyone goes back to their compartment, including Luna, who Hermione guides with an arm around her shoulder in a motherly/big sister fashion.
Harry eventually tells his friends that he's from the future and tearfully confesses that he's guilty of manipulating all of them. Cue group hug.
Then Ginny tops it a chapter or two later with this line:
Ginny: We were more than friends, weren't we? In the future, that is.
Sirius escapes and Harry reunites with him, telling him of the bad future he came from. Sirius remarks about the endeavor being one of the greatest pranks of all time and remarks. "Somewhere your father is grinning like a maniac."
Hermione makes a comment about people only wanting to be friends with her so she'll do their homework. Ron then immediately informs Hermione that he doesn't want/won't take her help with homework, because he wants her to realize that he's her friend for her, not for her homework skills.
After Melissa Bulstrode dies (in apparent revenge for her warning Harry about a couple of things) her sister Millicent starts to become bullied by her Slytherin companions and threatened not to tell anyone about it. Harry, feeling responsible (because he owed a debt to Melissa) finds a way to get her to go to Beauxbatons without calling undue attention, and funds her entire education there.
When Millicent returns during the Goblet arc, she has been taken under Fleur's wing, with the elder girl teaching her confidence and how to carry one's self properly. The main characters even manage to befriend the Beauxbatons students this time around, thanks to Millicent.
Percy loses his job in the Ministry after he attacks Barty Crouch Sr. when he's about to act after his son is revealed. His actions, though, help him land a much better job as Amelia Bones' assistant, since she respects him both for his bravery and for his smarts.