Have 1999 Pontiac grand prix 3800 engine. Car starts each time when engine is cold, but after driving a while and turning off car will not start until it is cold again . What is the problem?

Crank sensor and I believe yours has a heat sink for the ICM. There are plenty of other things as well. Does it ever die or just doesn't start up? Fuel pump could be swelling from heat and once you shut it off it seizes till it cools. Find out if it has fuel pressure, check for spark, and check for a pulse at the injectors.

Yes to the things John said and you can perform this test to narrow it down to ignition or fuel delivery. When the car is at a point where it doesn't start try cranking it over while someone sprays a shot of starting fluid into intake. If you now get ignition you have a fuel delivery issue. If not ignition. Such as crank sensor, ecm etc.