Idle speed is controlled by the ECU. When cold, the engine will be supplied with more fuel and air, but only enough to maintain the correct idle speed (ie. the same idle speed as when hot). Yours is functioning as it should. This system allows correct idle speed even with varying loads such as air conditioning cycling on and off. In my manual 190E I can even engage first (or reverse gear) and ease the clutch out and have the idle speed remain constant such that the car will drive at idle speed without touching the throttle. It will even reverse up the moderate slope of my driveway at 750RPM by way of the idle speed control.

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107.023: 350SLC, 3-speed auto, icon gold, parchment MBtex (sold 2012 after 29 years ownership).
107.026: 500SLC, 4-speed auto, thistle green, green velour.
124.090: 300TE, 4-speed auto, arctic white, cream-beige MBtex.
201.028: 190E 2.3 Sportline, 5-speed manual, arctic white, blue leather.
201.028: 190E 2.3, 4-speed auto, blue-black, grey MBtex.
201.034: 190E 2.3-16, 5-speed manual, blue-black, black leather.