Your insurance will pay you the market value of your car, unless you have premium insurance like Chubb. IF your insurance company pays you for the car, they will independently subrogate against the dealer to get their money back. If your insurance company pays you for the car, you have essentially been "made whole" and there isn't anything left for you personally to sue for. You can't get extra damages, punitive damages, pain, suffering or anything like that. You can only get economic damages related to the loss of the car. Your state law may be slightly different than where I practice, but I doubt it. Even to get economic damages, you have to show the dealership was somehow negligent in causing the fire. Not knowing all the facts, I think you would have a better case if the dealership returned the car to you, after claiming it was fixed, and it then had a fire. The dealership will argue that it was still "fixing" the issue, a known thermal event, and was non negligent in the fire.
Me personally, not as a lawyer, I wouldn't pay them for any services allegedly performed.
I think more concerning is the car had a thermal event. It seems this would have happened even if not in the shop's possession. What kind of car was it? Was it newer? I would report it to the manufacture. I'm very glad this did not happen while you or your family were in the car, or driving long distance!