Car dies when hot, won't start until cold?

i'm asking this question about my sisters car, it's a 1999 grand prix gtp, supercharged 3.8L. my stepdad has no idea whats wrong with it. the ignition control module was tested, and they said it was fine. it starts fine when it's cold, but after about 15-20 minutes it will die. we just tested the coil pack/spark plugs after getting it hot, and they all spark. other symptoms are-- when we were testing the spark plugs, when it would start, it would idle really low, and then spike up to about 2k, then drop below 1, almost stall, and then spike back up. my stepdad said it has done that before, and does it even with all the spark plug wires are connected, but when cold it runs perfectly fine. when trying to start it, if you push on the gas, it'll run, but really horribly. it blows a bunch of black smoke... but not when cold. you wouldn't even know anything was wrong with the car, until you drive it until it gets hot. also, according to my stepdad, the temperature gauge doesn't move at all. what are some other things we could test? my stepdad is in the process of swapping the ignition control module, and coil pack out of a different grand prix we have sitting in back.i don't have any hope that this is what the problem is, so what else could we try?