Will not start until it has cooled off

If it is turning over okay but not starting I would suspect the crank position sensor more than the ignition module as being heat sensitive is a known issue with them. The normal failure mode of the ICM is to give misfires as it heats up. A quick way to test if it is the crank sensor is to pour cold water over the sensor area and see if the engine starts up (also could be used on the ignition module to test it). You can also use component cooler or even "canned air" (wear gloves and flip the can upside down to spray refrigerant out). It is located behind the starter solenoid. Replacement requires you to remove the starter to get enough room to pull the sensor out without breaking it off.