If any way possible, try purchasing or get your parents to purchase a ReptiTemp 500R. It's the cheapest thermostat and it will control your temps pretty well and get them where they need to be by switching the dial. http://www.reptilesupply.com/product.php?products_id=75

The snake could overheat or burn at any time being on the area where the UTH is, and if the UTH is not controlled by a thermostat, temps can easily reach over 120F. It's happened to me a couple times before, but gladly I caught it in time so none of my snakes were overheated or burned. 78-84 for ambient and cool end temps is just fine, but that hot spot needs to get lower as soon as possible so the snake doesn't get overheated or burned.