During his Fan Friday where he plays Scribblenauts Unlimited, Jessie solves a puzzle by putting a mirror in front of a shoggoth. It gets frightened of its own reflection and gets upset. Jessie then spends the next few minutes trying to make it happy again.
Some of Jesse's interactions with Elizabeth during BioShock Infinite. Jesse genuinely likes having her around, partly since she's genuinely helpful. Makes one wonder what he'll do when he discovers Elizabeth's & Booker's connection to each other.
Giving a Rousing Speech to someone stressed about their upcoming exams is pretty damn heartwarming. Viewable here.
Jesse does his Sep. 22 2013 Revenge of the Q & A alongside his parents. It's both hilarious and heartwarming.
The Beyond: Two Souls playthrough has a lot of heartwarming moments, just because Jesse becomes so damn protective of Jodie.