My understanding is that wax motors are based on actuation - they are intentionally and deliberately either heated to extend or cooled to retract, and if ambient temperature is used as one endpoint, the other will not be ambient (i.e. a heating element or cooling peltier).
Thermostatic valves are ambient at both sides - they expand and contract naturally with the existing temperature, so they are not motors per se, because there's no actuation beyond the temperature.
Thermostatic valves are ambient at both sides - they expand and contract naturally with the existing temperature, so they are not motors per se, because there's no actuation beyond the temperature.