It looks like Micio has got the right idea there!
Yes, they do seem to do surprising things when trying to beat the heat. Mr. Me for some reason likes to get inside his cardboard box, Fort Mee, when it is especially warm. The box is in the same room with the wall unit air conditioner, but the opening faces away from the AC unit. I guess he doesn't like the moving air. Often he will lie on a rug right next to my bed. I thought it would be pretty warm there but when I've been on the floor to pet him it seems that there is some light air movement and it is cooler close to the floor, so he knows what he is doing. Right now, because of a major exam he had in May, his underside is shaved, and very little fur has grown back. So on some hot days that we've had, he will just lie on the hard floor with his bare underside against it. After that he can be quite cool to the touch!