I used to know someone who wore his Coonskin cap every day, even when the weather was hot. I once had to ask him if he got hot under that hat. He said yes and show me that it was drenched in sweat inside.
I've since learned to not want to see under people's hats.

Well, I'll admit I do wear a cap like Radar O'Reilly wears year-round, but at least with it being a knit cap, it actually allows for some ventilation... but yeah, coonskin caps, or sheepskin-lined hunting caps and such, those things certainly would bottle in the heat (and the sweat).