probably, but Im just throwing ideas out there. It might be that once the car has heated up there has been enough of a drop in fuel pressure that the car happens to shut off when the car is warm, not because the car is warm. Again, thats just my theory. Does the car restart after stalling or does it have to cool down first.
You should also do the pedal tap to retrive any fault codes, that might reveal your problem.
<span style='color:gray'><span style='font-family:Courier'>1995 e36 3 Series RIP
1999 e46 3 Series BURN IN HELL
2000 MR-S Roadster= Current</span></span>