The cadet heater has a built-in thermostat. How accurate it would be is, of course, pretty questionable; but before dabbling with too much wiring and switches and stuff, why not see if it is sufficient to just use its built-in one?
From the info on their web site, the built-in thermostat is simply wired to switch the main leads and the fan motor and heater element operate simultaneously (i.e. there's no thermostatic switch for the fan or other means of making it operate after the element is switched off). Switching the power to the unit with an external thermostat would make it operate in exactly the same way and would not cause any problems with the unit.
