the purpose of the thermostat is to regulate the UTH temp, theres usually a temp sensor in the tank that relays that info to the thermostat, and pending on the temp, the thermostat regulates accordingly to maintain a steady temp... so in your house with the fluctuating temps you should be fine, with UTH's using substrate is usually preferrred to prevent this, but it wouldnt go to the extent to cause burns on the snake unless it was a crazy high temp, which the thermostat prevents... so in any case your covered