Dave, the fuel check valve is part of the fuel pump assembly. Is it purchased separately from the pump motor? I feel like driving the car for 20 minutes would not significantly affect the temperature in the gas tank. Before I go there and replace the pump, I think I will spend time with the fuel pressure regulator as it is in the engine compartment.
The check valve is just a guess. The symptoms are difficulty restarting the car when it's warm. I'd suspect it would not shut the car down when the pump warms up. You're right - fuel wouldn't significantly increase temperature in a short period of time. Hot excess fuel is sent back to the tank from the fuel pressure regulator, however.
Like Colin says, the coolant temp sensor is on the head, near the front of the motor. There are two identical plugs there but only one will have two pins wired. Only one coolant temp sensor will have two pins. Be sure you put the correct plug on the correct sensors! Confusingly, the oil pressure switch uses the same connector as well. It's in the same area, on the side of the oil filter housing near the top. I have swapped those sensor plugs before, when I was doing the hose delete mod. The car ran normally, but the coolant gauge never moved and the oil light was on all the time, LOL.
Did you thoughogly check the hoses under the throttle body and the intake boot? Both are prone to cracking.
Are you sure the fuel filter is good, and installed in the correct orientation? Arrow on the casing should point in the direction of fuel flow, towards the engine. You could eliminate the filter as a culprit by connecting the two fuel lines together temporarily with a union (I wouldn't run it like that for long, and never with less than half a tank of fresh fuel).
