You need to control the heat !

Unplugging it is a quick fix, but you need the RIGHT heat going. Get a cheap thermostat (jumpstart/amazon) or at least a rheostat.

Keep the baby on clean paper towels. Clean and sterile. Nothing but hides, water dish and paper towels. Darken the enclosure by taping dark paper on sides, back of the tank (tape only on outside) Cover the top. Give privacy.

Vet, vet, vet.

You need something ASAP to prevent infection and to aid in healing. Silvadene creme is awesome, but is by prescription only..