While I appreciate the effort to incorporate science, I think your argument ignores a basic fact. Game of Thrones is not science fiction, it is fantasy. Magic exists in this world, and with magic anything is possible and even the laws of physics are free to be defied.
If Jon Snow can be raised from the dead, and Berric Dondarrion raised from the dead many times, if Bran can see everywhere (even into the past), if tree people can hurl fireballs, and so on, picking on the physics of dragon flight seems a trivial concern. Why not work on the thermodynamics of how the White Walkers’ undead Army can continue to move at all?
Speaking of thermodynamics problems your attempted explanation of dragon flight being that they are very hot produces more physics problems than it solves. Just what can create such tremendous heat? The energy requirements for that would be off the charts. If normal metabolic processes could even produce such energy, a dragon would have to eat many times its own incredible weight a day to do it.
If the heat inside a dragon is so hot it can melt stone then what is a dragon made of that resists it? How can something that tough even be penetrated by a spear or big crossbow?
For that matter, what of the similarly immune to fire Daenarys? What is she made of that confers her immunity to fire? Does she have asbestos skin? Her skin certainly looks perfectly normal.
The answer to all these questions is simply . . . “it’s magic.” Daenarys’ skin is like our own, except for the magic that makes it immune to fire. Dragon scales and organs are overgrown versions of similar reptile structures, with magic protecting them from their own fire (but not sharp weapons) as well. Ice zombies animate because of magic, without regard for the energy needs the laws of thermodynamics would suggest. There is no science that explains Bran Stark’s time spanning clairvoyance, it’s just magic. No science explains Jon Snow’s resurrection, just magic, and so on.
Dragons fly because they are magical creatures and flight is part of their magical characteristics.