1994 Ford Taurus starting problem after reaching operating

My taurus wagon has the following problem. When cold it starts with no problem and runs fine. However, when I shut it down and leave the car, for let's say an hour, and then come back it will not start. I then have to leave it until it is almost cold. Now the mechanic has replaced, coils, distributor, one of the computers under the dash. He also found a burn in some wiring that came loose and hit part of the manifold. The check engine light is not coming on and when the car is running it is flawless. This problem only happens when I stop it for a period of time. I looked in my haynes manuel and did some research on the internet. Do you think this could be a problem with the fuel relay that mounted in that box on top of the radiator? We are stumped at this point because he says he can not pull any codes on it without the check engine light being on. Also, this is an air force car that was used for security and you can start it without using the key they apparently disengaged that lock so if someone lost the key they could still start the car. It is the 3.0 engine.. Thanks.