What do heroic people do when they are hopeless and feeling very bad?

Any kind of feeling! either good or bad is pretty temporary in nature and will not last for long. Real heroes as you said to have definitely something special in them which made them the hero. It takes a lot of pain and consistency in achieving the benchmark. The Journey to heroism teaches them the importance of patience. So at bad times, they know that it will not last! they are positive, energetic and do not quit while patiently waiting for the good times to come. “Tough time does not last but tough people do.”