You said no fuel in the fuel filter, so start at the fuel pump. The electric may not be able to push fuel through the mechanical pump when it heats up, stuck valve maybe???
Bypass the mechanical pump for a few test drives and run off the electric pump.
Fuel should be flowing through the filter even if the carb is overheating. If the line is over heating, it must really be hot to vaporize fuel with two pumps running.
