All they have to do is tone down the fire to where Tadashi is running into a burning building and not just jumping directly into the flames. More like the burning building in the Incredibles and less like a bonfire. Something where it was believable that he could really believed he could have run in and pulled someone out.

EDIT: the way the fire was animated, it seemed less like taking a bullet for him and more like shooting yourself believing that it will allow you to save someone who's been shot