2000 Cavalier Shaking in Idle, Stalled in Park

My 2000 Chevy Cavalier shakes/vibrates pretty badly when in idle as though the engine is over-working/hesitating from stalling. It is a 2.2 li, automatic and has almost 52,000 miles on it. It also has just had the oil filter, air filter, fuel filter, spark plugs, serpentine belt and valve cover gasket replaced. I checked the battery too- that is fine. I thought it could be deposits in the fuel system, so after I filled up with premium gasoline I poured a bottle of fuel cleaner in the tank. Today I had the car on and in Park, the radio was on and the car stalled. The way I noticed the engine was not running was because the shaking had stopped. The battery light was on as well as the oil light. Although I just had the oil changed and checked. The battery was still running/on. Just after it stalled, I turned it completely off and then back on, it was fine, just shaking. I have also noticed the car does not shake/shutter as bad when I have the air running, but right after I turn the air off it sounds like it will stall but then I can hear the engine pick back up. Also, when I first turn the car on it takes a few minutes for it to start shaking, when I shift from Park to Drive it does not shake at first, it takes alittle while. When I came home I had it in Park again and left it running for approx. 10-15 minutes to see what would happen, it didn't stall but the temperature did rise 2 notches from 195 and it was still shaking. Please help.

give us a little more info, like engine size so we can better help you. Also, if you can be a little more specific as to the symptom. Has the car restarted since it last stalled?