Should I be concerned that my cat has been spending hours at a time in the hottest room in my apartment?

Background: I don't have central A/C, so I have to rely on a (shitty) window unit. The bathroom is at the opposite end from the window unit, and we (my girlfriend and I) keep the door closed in order to keep more air in the main room. The room temperature in the bathroom is easily 80 degrees plus and also quite humid.

If either of us go to the bathroom, the cat will follow us in there and not come out. Normally, I wouldn't care, but it's just so hot in there I don't want him to get heat stroke. Do cats just naturally have a high heat tolerance? Is he fine, and I'm just overreacting? FWIW, I try to only let him enjoy his sauna when I'm at home so I can listen for him scratching at the bathroom door and let him out when needed.