You ask a good question for which there is not a simple answer.  Because there has been so little research done on TMJ, there is no dental or medical specialty that is specially trained to treat it.  There are, however, both doctors and dentists who have experience treating TMJ and some even call themselves TMJ specialists. 

The TMJ Association recommends seeing your primary care physician first to rule out any other possible illnesses that may be causing your symptoms.  Personally, if I were pretty sure I had TMJ, I would probably start with a dentist who has experience treating TMJ.  For one thing, dentists have the equipement on hand to do panoramic x-rays, which can help identify the source of your problem.  They are also the ones who make mouth guards if you need one.  Should you need more extensive treatment, they may refer you to a physician. 

I wouldn't just go to any dentist or doctor.  Call around first and find someone who is experienced in treating TMJ patients.  Whether you see a doctor or dentist, the TMJ Association has a list of questions you should ask before consenting to any treatment.  Here is a link to that list:  http://www.tmj.org/treatments3.asp

Good luck!