It has been VERY hot here for the past few days...in the 90's!, and sunny. And I do feel you are right about keeping Fozzie inside out of the sun. I've already seen some irritated-looking scratch marks on him. I'll get a large cotton tee shirt and tuck it in for him.
My good friend, this morning, while visiting, mentioned the very same thing you said about fur providing insulation.
thanks!
Patty