Does the heater make a distinct although not necessarily loud click when it kicks on or kicks off as you slowly turn the termperature knob back and forth (manually) with or without the heater plugged in?
If not then the heater may be one of the few models that does not have a snap action thermostatic controller. This makes for a longer arc at every kick on and every kick off and more internal wear and tear. For this the external voltage controller may make sense.
Or do you notice more even room heat with the external voltage controller in use?
Otherwise the external voltage controller, even a cheap Chinese model, is an unnecessary expense item.
Except for the situation I mentioned, resistance electric space heaters do not need voltage regulators let alone regulators that anticipate and/or second guess the heater's behavior to reduce the need for the heater to kick itself on or off.
That said, I have made "portable thermostats" in the form of an "extension cord" (of suitable amperage) with a box in the middle holding the line voltage wall thermostat. The purpose was to operate an electric space heater whose controller had failed (stuck on) for the above discussed reason.