Mainly, fuel pumps heat up because the electrical system is still working, and internal friction between moving parts. While running, these pumps work non-stop as long as the engine is on, consuming approximately 12 volts of power for every 30 seconds, which creates heat. Moreover, fuel pump operates by pushing the fuel at a higher pressure (typically 30 to 80 psi), which creates internal friction. That friction, with the associated electrical energy, translates to more heat generated by the pump, with long distance drives particularly contributing to this problem.
This problem is worsened when the fuel level is low. The pump needs petrol to cool itself and without a quarter full, there will not be enough petrol to flow around the pump to keep it cool, as the petrol is running round the pump it absorbs the heat from the pump. Without cooling, temperatures can increase, causing lower efficiency, and ultimately proclivity for shortening the pump life by 30% or more, especially when operating hot on a continuous basis.
The pump can also overheat if there is dirt or debris in the fuel. A blocked or clogged fuel filter or dirt inside the pump causes it to work harder, which increases power consumption and the internal friction. Replacing old fuel filters every 30K miles will prevent clogging, and excess heat, per maintenance guidelines.
Where performance is concerned — like in motorsports, for example —fuel pumps are also under even higher stress levels, smothered by a constant, heavy demand. Because normal pumps are almost guaranteed to overheat under the elevated load, race cars tend to use specialized cooling systems for the fuel system. If you think this doesn't translate into the automotive aftermarket, you're mistaken: performance-minded fuel pumps frequently include a cooling solution of their own, and for others, they're mounted externally to preclude overheating.
Scotty Kilmer, automotive expert explains this in his maintenance tips: "Driving with an empty fuel tank or a clogged filter is like driving your engine without oil. Faster temperature rise and faster wear. [sic] An overheated Fuel Pump can lead to premature failure and engine misfires — but maintaining appropriate fuel levels and replacing filters regularly can keep the Fuel Pump cooler and prolong its service life.