This Headset is really good and on a deal on Amazon today....
https://www.amazon.co.uk/Sennheiser-PC320-over-ear-gaming-headset/dp/B005HWEZ02
They are over ear, so comfortable, but open backed so not too hot, and the quality is good for music as well.
I tried about 4 different types, including some really expensive ones, and these were the ones I choose to use daily.
Re. the sweating, I always had to wear a sweat band or I would soon be blinded, even with a massive fan and open window in winter. Wringing them out after a Mountain Goat climb was always shocking!