Does your character have something to lose?
When I thought about it later, what struck me about the difference between this film and the past ones was that this time Tony Stark truly believed he had something to lose, something that mattered more to him than his own life. It also cast him in a new light, less bravado, more kindness. The possibility of loss made him into a better person.
I decided to put my own lead character to the test. Did he have something to lose if he didn't rectify the situation he found himself in? Firstly, he had his old life to lose. He thought that mattered to him. Secondly, he had his new friends to lose, their respect and possibly their lives. It surprised him how much that mattered to him. This new concern, this new possible loss, laid him bare. It made him vulnerable but it also pushed him on to try. Having something to lose turned him into a hero.
What about your characters? Do they have something to lose and are they better for it?