1993 Eagle Vision - restart problem

I have a 1993 eagle Vision TSi that runs well for the most part, but has one fustrating fault. The car has no problem starting first thing in the morning, but after it is driven for awhile, even just a 20 minutes drive, it won't start again until about 30 minutes has gone by. It seems that after it gets warmed up it has to cool down before restarting.

The engine is a 3.5L 24 valve which has only about 65,000 miles on it. The engine was replaced in the car.

I have taken it to mechanics and they cannot seem to find the problem. The car did have a factory theft system in it, but that was removed, or disengaged.

One person told me to replace the fuel pump to start with but that seems like an expensive fix not knowing if that is the problem.

The car does run really well, it has stalled twice over the past two years where I have got caught in the traffic while waiting at a traffic light. I had to wait 30 minutes and then it starts on it's own. Both times it stalled the weather was hot. But again, it runs well when it's running.

Help please, Bill