Does Sauna or steam damage hair?

I recently saw a video of some guys hitting the sauna (why I am watching other guys going to the sauna is another story), and they received this kind of hat at the entrance. They said it’s to protect their hair. Been doing Sauna for a while and have never seen that. I did notice how my hair would get super hot like it could almost burn my finger. So yeah, I was wondering what is the risk there? Usually, you hear it’s good because it makes blood circulate, etc. Side question: would the steam room be better if the sauna is damaged?

No, neither a sauna nor a steam room should damage your hair. Remember, the hair on the head is not alive; only the hair-manufacturing apparatus beneath the scalp is alive.