Comment by alias_neo

I think the fuel passing through is the only method that could be used to cool, the volume of fuel required is presumably constant, regardless of how much fuel you have left, so the amount passing through the pump should be the same until you run out.

On a related note, my car has a fuel heater, to pre-heat the Diesel before it hits the engine, I assume this is typical in modern cars, but using the fuel as a coolant would presumably contribute positively to this desire for warmer fuel entering the cylinders.