Dany sat in Khal Drogo's funeral pyre until it was nothing more than ash and a few smoldering logs. Outside of her clothes burning she was unharmed. S1 E10.
In S6, don't recall which episode (close to the end of the reason) she walked out of a building that burned to death everyone else inside. Again, clothes were burned but she was completely ok.
Targaryen's are not fire proof. Dany is something different. Something super-natural. Getting in a scalding bath tub is irrelevant compared to the fires she was been and walked away from unharmed.
Dany has to be Azor Ahai. If not, it's the biggest head nod GRRM built in to this series. Which could be the case but I doubt it. I think it is so obvious, like R + L = J, that we tend to doubt it to be the case. Regardless, no one can deny she is something more than mortal. And.....she's gone by the name "the Unburned" since book 2, season 2, for a reason. IMO of course.