I haven't had the sensation of heat, but I get a lot of weird pains in around and behind my eyes. Sometimes I feel pressure, like my eyes are bulging out of their sockets. Other times is a combination pressure and a very odd painful sensation...it might be one of heat. I'd say the odds that your sensation is MS related, but I would not hesitate to see an ophthalmologist to make sure it's not with your eyes per se.

A lot of facial/eye pain comes from the trigeminal nerves just in front of your ear, and spread in various tracts across the face, eyes, cheeks, mouth, and can include what feels like tooth pain. (I know because I have all of these from time to time.)

I also know how uncomfortable it can be. Hope you are feeling better.