Electrical concerns aside, fuel pumps are heat-sinked by a rather large quantity of sloshing fuel. Can't see a slight increase in heat produced making them much hotter. They fail when people run them dry - that's when they get hot.
The increase in resistive heat assumes an increase in current, which highes on a substantial decrease of inductive back emf. That is true for the case where shaft speed is reduced through application of a load - thus deflecting shaft speed from the free speed. In our case, simply decreasing the voltage (which by nature lowers the free speed of the motor, as well as the speed under load) at the SAME load does not produce the same effect.
Again, what if you were to use a 14 volt battery system rather than a 12 volt system? I just don't think a battery charger (or a power inverter) is going to be able to keep your primary charged when considering the loads of the vehicle.
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