2001 Pontiac Grand Am '01 Warm Start Problem

I have a warm start problem with my '01 Grand Am V6. The engine will turn over and fire momentarily, but it will then die. After that, no amount of cranking will get it to fire. I have to wait an hour or two for it to cool down, whereupon it will fire right up and run as if nothing happened.

This happens randomly. Sometimes just a short trip to the store will make it happen.

The fuel pump relay was replaced, no effect. A repair shop couldn't reproduce the problem, or find an error code. They sold me a fuel filter, which didn't help either. They wanted to sell me a fuel pump, but I don't think that is what is wrong. I can hear the pump working when I turn on the key, and the valve on the fuel rail squirts a strong stream of gasoline those times when this happens. Also, there are no fuel starvation problems under other conditions, even when working hard in the mountains, only when I try to start it warm.

Since this is a temperature-related problem, I pulled the connector to the Coolant Temp Sensor to see if that would make any difference. It didn't, but I replaced the sensor anyway. No luck. Is there another temp sensor that I might have overlooked?

Searching the internet, I find failure to warm start is a common problem with this model, but didn't find any verified fixes. I hope that I will find one here! I don't want to replace the expensive things without some logical plan.