5.7 liter starts cold does not want to start warm

Check the doors in heater/ac box sounds like it is working back and forward between the hot and cold vent. Can't remember if they are vacuum operated or not.

Do you have normal fuel pressure when you first crank it ?

sounds like your coil is getting hot then when it cools down the engine re starts check coil look for hot spot or touch it see if it is hot it should be cold.

Hi Austin, I think you hit the nail right on the head! Replace the glow plugs:-) Regards John

Possible bad cold start valve or the sensor that tells the valve to activate when cold. Start by replacing the cold start valve first.

What faults codes are showing on a test of the electronic engine control module?

It sounds like the fuel pressure regulator is bad.

these have a problem with the overhead cams, one or more of the bolts break which restricts the oil flow to the lifters.

You need to check a service manual on this but it sounds a bunch like a cold-start valve isn't closing once the engine is warm and this would cause an overly rich fuel-air mix that would gag a warm engine. I don't know if your car is equipped with  one or not. 

If it starts with a shot of WD-40 then fuel delivery is obviously a problem when cold. If intake air temperature sensor ( for one) is telling it that its still real warm out, then it won't give it enough fuel to start on a cold day, which requires more fuel.