I agree with the suggestion for thick walls to help retain heat while brewing pu'erh. But to be honest, I think that this parameter will not affect the brewing very much.
I have a couple of gaiwans at the 120mL size (4oz) and that size works really well for me as a person who drinks pu'erh alone. I would take size into consideration because you'll often be going 10 steeps, and the size of the gaiwan will drives how much total tea you're drinking over all of those steeps. Hopefully you have some idea of what you prefer (or what you can stand) from previous tea sessions.
As for burning fingers, I think the biggest 'trick' is to make sure that you're not filling the gaiwan to the brim. If you fill the gaiwan to the brim, you have two ways to burn your fingers -- the rim of the gaiwan will be very hot, or hot water/tea will spill out and hit your fingers as you pour out the gaiwan. If you avoid filling the gaiwan to the brim (but still fill), the rim will be warm, but you won't burn your fingers. And... nearly all gaiwans should have this property with their out-turned rims.
Hope that helps...!