89 300se stalling problems

[Maddog]

Well I have searched all of the forums for answers about stalling problems and I have still come up empty handed. The car that I am working on starts up fine and runs fine for a while. As the car begins to warm up though the idle begins to jump around and the minute that the car is in gear and stopped, the engine dies. Yesterday I went over and started to diagnose it with it just sitting in the driveway running. It got to a point that it was running so badly that it backfired and then died. I don't even know where to start.

I am thinking it may be a combination of dirty fuel injectors with a bad fuel pump relay. Is there a better way to clean injectors besides just running injector cleaner through the fuel system.

Would a bad coolant temperature sensor cause the car to run this badly?