You're a dingus who doesn't understand that they can only release heat through those small areas. They can still absorb and contain heat with the rest of their body.
Imagine if you could only sweat through your face. If you were naked, you'd be cool. If you were wrapped in a fur coat and plastic wrap, you'd be much warmer, with the same limited amount of heat release.

They can only sweat through their nose, tongue and foot pads. He's wrapped in plastic. I do think so.