I would say there is a way, but will likely require slicing into the blower power supply inside the heater. (there goes warranty).
You would also want to make sure you aren't overloading the wiring inside the heater.
Safest alternative would be wiring something In With the thermostat and maybe using a relay and separate power tap to power the fan.
I would say all in all a pretty complicated solution that would be above my skill set.
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