Wow! Sorry for the dilemma. Yeah, even though you are seeing healing externally there could certainly be a problem internally. IMO, i would make a appointment with a exotic vet bc this extent of a burn may require not only antibiotics but specialized wound care. Even if you just get the vet to look at it and get a professional examination. Then see what your options are. P.S. Turn off and unplug the heat mat until you can get a thermostat so as to avoid further injury.