A thermostat is a device that measures the temperature of a heating device and adjusts according to the temperature that you set it to automatically. It comes with a probe that measures the temp. If the temp gets too low, it kicks on, if it gets too hot, it kicks off.
A thermometer is a device that only reads temperature, it does not adjust it in any way
A Rheostat is basically the same thing as a dimmer. It reduces the amount of power going to the UTH making it hotter or cooler. The problem with using a rheostat is it doesn't know when it gets too hot or too cold, you have to check it a few times a day and adjust it accordingly. The thermostat takes out the constant adjusting.