Thor and Jane's reunion, after she stops slapping him.
Frigga's relationship with Jane and protecting her from Malekith to the point of sacrificing her own life. It's been established that Jane's relationship with Thor is futile due to her much shorter lifespan, but Thor's mother will defend her because she is the woman her son loves. Doubles as a Tear Jerker.
Sif and Volstagg being protective of Thor was just precious.
In the scene where Jane is being examined, Jane and Thor keep exchanging smiles.
More specifically, when Jane correctly guesses that the tech they're using on her is a quantum field generator, Thor's proud that's-my-girlfriend smile is just adorable.
When Odin takes Thor and Jane into the library, explaining about the Dark Elves, Thor recalls the story in saying, "Yes, Mother used to tell us stories as children." Us, as in, he and Loki. It's small, but it shows that Thor hasn't forgotten his brother or the times they spent together.
The very fact that Loki still cares about Frigga, and was very willing to join Thor in avenging her.
Frigga and Loki's entire relationship - she begs Odin to spare him, and then visits him in his cell against her husband's wishes, bringing him books and trying to make him comfortable. She's the only one in the movie Loki seems to value and doesn't lash out against. It's also very telling that she's the one who taught him magic - young Loki must've felt very insecure under his father and brother's shadows, and Frigga gave him something that was his own.
Frigga says exactly this in a deleted scene: Odin and Thor cast very big shadows, and Frigga wanted Loki to "find some sun of his own." She says this in response to Thor asking her if she regrets teaching him magic, and her response is no, even after the way Loki has used the power she gave him.
When they're in the Dark Realm and Jane is still unconscious, Loki starts to question Thor on him choosing her; he says that she's like a moment in their long lives, and will be gone before Thor knows it. What makes this heartwarming is that Loki appears genuinely concerned about his brother, knowing that Jane will only cause him heartbreak.
In the same scene, after Thor and Loki have an argument about Frigga, this exchange happens which is both heartwarming and giggle-worthy:
Thor: No... [Mother] would not want us to fight. Loki: ...Well, she wouldn't exactly be shocked.
Right after that, Thor gives him a small fond smile. And if you look close enough, you would see Loki giving him an even smaller one.
Despite everything, Thor says "I wish I could trust you." And Loki seems affected by it.
Loki's reply, "Trust my rage." The whole exchange is a perfect Crowning Moment of Heartwarming.
During the battle against Malekith, Loki sees Kurse throw a Black Hole grenade at them. His first reaction is to push Jane aside even if it means he'll die. Heartwarming in that he had no gain in saving her; it was like an instinctive reaction. He also sheltered her when the Aether appeared to explode. There are many possible interpretations of this, three of which are: he was saving the girl his brother loves, meaning he still cares for Thor despite his claims otherwise; he genuinely somewhat likes Jane, like he had said earlier; or (most probably), his mother had sacrificed herself to save Jane, and out of love for his mother, he would not let her sacrifice be in vain.
Then Thor saves Loki. Most importantly of all; in spite of all his claims to have severed kinship with him like Odin has, Thor still loves Loki dearly in spite of himself. Especially heartwarming are the quick looks they exchange after this.
Then Loki saves Thor. Watch his expression when he sees Kurse beating up Thor. It's a 'nobody gets to attack my brother except me!' face.
There's also (possibly) the dialogue as Loki 'dies.' Made heartwarming as he has no reason to lie at this point, though it's Loki, so you can never really tell.
At the end, when Loki is impersonating Odin on the throne, he genuinely, if he wanted, had the chance to turn the tables on Thor, and throw him in the dungeons for committing treason, and none would have questioned "Odin" on it. What does he do instead? He tells Thor he's proud of him, and lets him go. Sure, he's not really Odin, but despite finally being on top he chose not to completely screw his brother over when he had the chance, and even make him feel like he has the fatherly affection Loki never had.
Also, Thor kept his promise to Loki by telling his "father" that Loki died in valiant combat like any honorable Asgardian.
Thor unknowingly telling Loki that he would have been a better king and praising him in front of (who he thinks is) their father. That might have helped in Loki's decision to let Thor go and even praise him as he's leaving. And even though he says "Thank you" in a menacing tone, he could have partially meant "Thank you for finally acknowledging that I am worthy of something."
The Stinger is very heartwarming and funny. At the beginning of it, Darcy and Erik try to comfort Jane because Thor didn't come back. Then there's a storm and he arrives on the backporch. Cue kiss.
In its way, the relationship between Malekith and Algrim is pretty sweet and caring. They're clearly fire-forged companions and while Algrim's self-sacrifice is ultimately for a pretty terrible cause, his total trust is pretty touching.
When celebrating the recent victory, Volstagg is shown surrounded by adoring children and holding a young girl on his lap. The credits list the children & woman as his family, which makes it all the more heartwarming.
Hogun the (normally) Grim smiling happily when Thor tells him he should stay on Vanaheim for a while with his people.
The way Loki still calls Thor "brother" despite claiming that Odin is not his father and being still pretty messed/torn up by The Reveal.
To drive home the point, Loki furiously denounced Odin as his father, and hesitated before saying the same to Frigga, but it never even occurred to him to stop thinking of Thor as "brother".
Sif is strongly implied to be in love with Thor, who loves Jane. However, Sif never lets any jealousy influence her, and during the escape from Asgard, she is the one who gets Jane out of where she's being kept and later escorts her.
Jane tries to drag an unconscious Thor out of the path of a giant falling spaceship, but he's too heavy to move away in time. At the last minute Jane throws herself on top of Thor: shielding him with her body as much as she can while ensuring that they'll die together.
Natalie Portman wanted to return for this movie and signed on, but couldn't work on it at the time due to being on Maternity Leave. What did the production team do? Why, hold off on making the movie until she could participate, of course!