If heat is all thats helping, it could point to muscle involvement which could be compressing the nerves or it could be due to clenching from the TMJ, again I'm speaking from my own experience here. If it were me, I'd reach out to whomever is treating the TMJ. I've had injections before into the joint which are extremely painful, but they do calm down the pain for a bit and help break the cycle. If its ON, then there are nerve blocks they can do to also help, and there are medications but you need to get a handle on whats causing it so a neuro is probably your best bet. Hang in there and post when you find out what it is. You are already scheduled to see a headache specialist so that should also help you determine what the problem is. I think most of them are neurologists so that is a good thing. Take care