I am not a vet, so I will leave medical advice related to tube feeding, feeding frequency, and burn treatment to more experienced members. I would recommend following the advice of your vet. If you want a second opinion, are there any other reptile specialists in your area you could contact?

As for the "culprit", were you able to get the heating issues addressed? You don't mention it but I assume your tank/enclosure is heated by an under tank heating pad. Is it regulated by a thermostat? Since you ask for any advice, my best advice is to make sure your heat sources are regulated so the burn can't happen again!