Using 15 amp thermostat on a 20 amp circuit
You cannot compare this question to the allowance of a 15A receptacle on a 20A circuit. This is apples to oranges. 

You can have as many 15A switches, thermostats, controls, etc, on a 20A circuit, provided the load each item is controlling is within its own rating. 

So you can have a 15A thermostat, controlling a 10A load, on a 20A circuit.