There are several different directions to go with this-It could be caused by an electrical component such as the coil or ignition module that is breaking down under a heat soak but while it would explain the backfiring, an ignition problem woudl surely set a code.
Those cars also have a tendency for the belt tensioner to be bad, causing the alternator not to spin evenly, and creating a large amount of stray AC leakage or ripple on the DC circuit. This condition could be worse when the car is warmed up and after the engine has been runnng-the internal alternator components can break down with heat like the ignition components and this type of symptom will result. This issue can be going on without any indication of a problem in the charging or starting system-AC ripple can be tested and the waveform read to determine if there is an excessive amount.
The problem could also be the catlytic converter. If the engine does not rev up easily when you step on the gas and seems to have a hard time getting the RPM's as well as the speed up, then that is probably the case. This can be checked by a manifold vacuum test-if the vacuum decreases or does not raise under steady engine acceleration then a restricted exhuast is the cause.
If you can give me any more details about the problem, when it started etc. I can give you a more accurate answer. The more details the better-I'll be glad to work with you a step at a time to eliminate the poosibilities.
Hope this Helps. Thanks for using JA
Well wether you think much of it or not, I have encountered this problem in many many V6 GM motors. And I didnt arrive at that off the top of my head, due to the fact that there was a recent $500.00 tune up done and there is still a problem lends validity to that as well.
After several years of fighting with these engines, I started to see a pattern develop with alternator ripple and ignition system issues. Like I said, it doesnt have anything to do with the alternator charging or not. The alternator is what supplies the 12 volts to run the car, when diodes or diode bridges fail, AC current is allowed to travel along the circuits and it creates havoc for the computerized engine controls. Invariably, the vehciles that developed this problem had tensioners that were original and had been on the cars for years. Usually you won't even know the tensioner is bad until you go to take the belt off and find that the pulley is positioned way off from where a new one would be. I have attended training specifically on the 3.1, 3.4,and 3.8 engines and have worked on literally hundreds of them-there is a whole chain of events that starts with the peice of crap tensioners GM puts on them.
The catalytic converter, if it is restricted, may not be resricted enough to create problems cold, but if excessive heat is building up in front of it, the harness and components that are located on the back side of the engine ( or engine compartment) get overheated and I have also seen this as an issue repeatedly.
You should also consider the possibility that you are having a fuel pump issue. If the pump is failing it will get worse as it runs longer, and that would also cause the sypmtoms you are describing.
Let me know what you find out. Thanks for using JA