To be quite honest, many people don't use thermostats. Most people don't know about them and petstores don't usually sell them or even tell you to use them.

Will the snake die? no. Will it thrive? no. The snake should be in a controlled enviroment with heating control to make sure it doesn't get burned.

Is the snake on reptile carpet? If so, it won't get burned. The only problem with reptile carpet is it is a breeding ground for bacteria, smelly, and impossible to clean.