Agreed in regards to the thermostat. I attached a low wattage mat once to a tub without a thermostat to see what would happen (no snake in tub) and 2 weeks later, there was a hole burnt through the bottom of the plastic so you can imagine what would have happened if the snake was there. They can be deadly without a thermostat. I've also attached the stick on ones to the bottom of glass aquariums before and within days, they're too hot to touch with your bare hand and since snakes and often ball pythons, generally will push the substrate or paper towels out of the way and sit under it/directly on the heat source, they become extremely dangerous. Just my experience with them - i would definately recommend a thermostat. Amazon sells inexpensive hydrofarm thermostats that are great if you're just regulating one enclosure and they're only $30!

I would clean the snake and apply triple antibiotic ointment to the scales, gently rubbing against them so it gets under the scales. Clean and re-apply in the evening. Make sure your husbandry is spot on - in general - but it's super important right now while your snakes healing. Clean water daily and replace paper towels daily and as soon as there's any spoil.

Good luck!