Just as a clarification, this may be the case with the automatic climate control system (with horizontal row of buttons and single temperature wheel) on North American delivered W124s. On the "manual" climate control system we got in Oz (as shown in previously posted pic) the compressor only engages when the cabin temperature is high enough to demand it. To have it operate at low ambient temperatures to reduce humidity (ie. at same time as heaters) the "demist" function (uppermost of the three buttons) must be activated. The only other situation that would operate the compressor together with the heater would be in the (unlikely) situation where the temperature wheel for one side of the car is set to a significantly lower temperature to that for the other side. The EC mode (middle button) disables the compressor.

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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.