[QuantumMotorsports]

Sounds like it's just another case of ford electronics being bastards. Man, I've had three 5.0 EFI cars and ALL of them did stupid stuff like this. One wouldn't idle at a steady RPM, I checked and/or replaced everything I could think of, O2, Idle air valve, TPS, EGR, TFI, Coil, Timing, ignition pickup in the distributor, etc. Then the same car would start hesitating and stuff. My next car would just randomly die while sitting at a stop light. Or right as I would hit the gas to leave a stop light, it would die. The only way it would restart is if I cranked it with the pedal to the floor and it would start. Finally figured out that was my TFI was messed up and the only way to make it fire was when it thought it was at WOT. Anyway, your problem sounds a lot like either the TFI or I've had the pickup coil in the distributor go out and it does things like what yours is doing. When it got hot, it would sputter and die. Then sometimes restart, sometimes not. If it cooled off most of the time it would start again. I finally just replaced the whole distributor because the bearing was all sloppy in it anyway. Well, I hope you enjoyed reading that little novel that I wrote. Good luck man!!!