You want to have a thermostat to keep the temperature of the UTH in a safe range for the snake. After a day or two, when you're sure the temperature stays where it should, you can put the bedding over it with nothing between the glass and bedding, and put the snake in.
If the snake burrows down and lies directly against the glass where the UTH is, it won't be burned because the thermostat keeps it at the correct temperature.