Stalls during summer at traffic lights or in traffic jams on 1997 Chevrolet Cavalier

My 97 Cavalier stalls after driving in traffic (constand idling and low speed driving) during summer time. Temperature sensor goes approximately to the upper third part of the gauge or higher when it happens. Engine starts to shake and then stalls completely. Also, another symptom is that after heavy rains sometimes it's sort of coughing/half-stalling when I first start to drive, but after driving for a minute or so goes back to normal. Did anyone have same symptoms?
I took it to a couple of places, but they couldn't diagnose the problem.

Asked by for the 1997 Chevrolet Cavalier
Does the engine in your Chevrolet Cavalier start right back up after it stalls or do you need to wait a while before it will restart?
When it stalls after shaking and losing power, if I try to restart it right away -it starts with strong shaking and quits after a few seconds. I have to wait for a few minutes, then it restarts OK, but if I keep driving under the same conditions (stop-and-go) - quits with shaking again within a minute or so. The only way I found out to deal with it - wait for a long time (30 min or so) and then try to drive a few more miles in the stop-and-go.
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We also have a 97 Cavalier. It starts hard in the rain, keep pedel down while starting. We got rid of the airconditioning because of the stalling, never to have it return. Ours has 240,000+ miles on it.