Proportional thermostats will NOT work properly on a generator...
Proportional thermostats use an electrical component called a Triac to regulate the amount of power going to the heat source (basically the heart of a Proportional thermostat)
Triacs must have a stable Sinwave like the one that the power grid operates on. Generators do not produce the same waveform.
The thermostat will appear to be functioning (it does indeed have power) but the amount of heat being produced will not be what the thermostat thinks it is putting out. I can get more technical if anyone wants but I don't think that it is necessary.