Cooling the output should increase the Carnot efficiency of the motor.
Heating the outside air intake with that heat should be sufficient to avoid the need for an electrical resistance pre-heater.
This combination could also run on propane, ethanol, gasified wood, etc. Anything that gets burned now could be used to create far more heat output than straight up combustion.
There's got to be a flaw in this idea, math/physics wise.