If you are using a glass-encased heater then it may help to replace it with plastic-encased heater, glass has much higher thermal conductivity than plastic which means it transfers its heat much faster to anything directly touching it, which is usually water - but in case of prolonged contact it could also burn the skin of a fish; the temperature regulation of plastic-encased heater will take a bit longer time to stabilize temperature changes, but overall energy efficiency should be similar.
Also, a heater is extremely simple device that doesn't have any modes of operation beyond ON and OFF; a thermostat facilitates maintenance of stable temperature in the bulk of water column, but doesn't control immediate power output of the heater, thermostat only controls the duty cycle of the heater; if you set your thermostat on a temperature higher than the current temperature of water, then no matter what value you set the heater will blow with full power output until that temperature is reached, then it will turn off and after some time once the temperature drops a bit below what is set on thermostat it will start to blow with full heating power again and repeat the cycle; this also exhibits a thing called hysteresis, which means it oscillates a little above and below the set temperature to decrease the frequency of on-off switching and thus extend the life of equipment.
As for the wound healing I would suggest using some product that enhances slime coat production of the fish skin, this is usually in a form of concentrated liquid added to the water; I know it could also help to temporarily increase salinity of the water to prevent secondary infections during the healing period, but I don't know the exact formula of optimal salt concentration. Also, to completely prevent these burns from happening in the future again you could switch to under-gravel heater or use a separate second tank with only a heater in it, then connect it with the first tank via pump and pipes. One more thing suggested in a comment by Allerleirauh is to separate the heater by enclosing it in a little cage to prevent direct physical contact with the fish.
Additional information that was missing from my answer about this subject was added by Trond Hansen in a comment (I only fixed punctuation, etc.):
It is best to put the heater at a spot where the water is moving to keep the surface of the heater as cool as possible. The concentration of aquarium salt should be 0.3% which equals to 300 grams of salt per 100 liters of water; this concentration is safe for continuous use in a fish tank. Many types of dechlorinators contain additives to protect the skin and gills of your fish. The most important thing to do when your fish is injured is to maintain a good water quality. Do not add antibiotic or antifungal medication - it will disrupt the biological balance in your tank. Also, do not use table salt in your tank as this contains potentially harmful additives, use only aquarium salt from your pet shop.
