[quote=@Muttonhawk]
But before I give up...I also had another thought! Many creatures have a cluster of blood vessels around the nasal cavity as a means to cool down, right? Well, hain beaks have a lot of extra space in them. Maybe they have a larger version of that cavity than normal so it can provide better cooling?

Wow, am I thinking about this too hard. This is a mistake.
[/quote]

Ah, yes, nasal cavities. Hain have plenty of space for those.

I had another idea for hain cooling. Hain probably have a few joints and stuff where the soft flesh is relatively exposed. These would be good places to put dense networks of blood vessels near the surface to allow for extra cooling. Cooling would be driven by sweat glands and/or manually licking the skin ([url=https://asknature.org/strategy/foreleg-licking-cools-skin-2/#.WOxQB9KGOUk]like kangaroos do for their elbows[/url]).