How can I retrofit this existing wall-heater with an external thermostat?
I think what you have is a mechanical thermocouple sensor that is connected to the regulator. This is the same as one would have in an RV. They do not use any electricity, and the thermostat is part of the gas regulator. The only remote I am aware of would be a remote thermocouple. I'm not sure if your unit has a removable sensor. If it does, then you can place the sensor elsewhere, but you will still have to set the desired temp on the dial in the unit. There is no actual remote thermostat for this type of unit that I am aware of.