Low idle and stalling but drives ok under power

Hi Saab 9-3 se convertible year 2000, 120,000 miles: Car idle is 500 should be 1000 sometimes stalls but drives ok. Cut out in park, when a/c on, lowering hood, closing hood, ok when revs are 1000, revs low 500 in park, when I stop, etc, sometimes stalls, cleaned throttle body, service i.E. Oil, fuel filter, air filter, oil filter, oil, plugs, still tick over is 500, also can you tell me sounds silly should the engine get hot so quick? Temps Gage sits in the middle where it should be? THANKS FOR YOUR TIME, TONY