Thisscene, in which Jack protects Reilly from the Doctor's robots. He really cares a lot about her at this point, and it shows. It gets even better when she herself decides to protect him afterwards. Teamwork between former enemies is always nice. For these two though, it was downright heart-warming.
Even out of context, this page looks sweet (possible spoilers though.) But, when you know the story behind it, it becomes even more heartwarming. Mr. Porter has endured his own personal Hell for years after the Doctor brainwashed him and made him kill dozens, maybe hundreds, of people - starting with Sonia, the woman Jack loved. He's been completely aware of everything that's been going on, but unable to do anything to stop it. Though he did try to gain influence for a long time, it wasn't until he met Reilly, someone who reminded him of who he used to be, that he really began to regain control and become himself again. She inspired him to have courage and never give up hope. She helped him free himself. If that isn't heart-warming, nothing is. May also count as a Tear Jerker.