At idle, the air sensor pot should be in the same position whether the engine is cold or not. So I am not sure if this is the most likely cause of your problem. However, a wrong air metering signal could for sure cause an inapprorpiate air/fuel ratio.

Check also the coolant temp sensor, also called fuel injection sensor. On my 87, 260E, it is the last sensor on the engine, closest to the windshield. When engine is cold (20 degC), the resistance across the sensor should be about 2.5 to 3.5K and when the temp is about 80 deg-C, the resistance should drop to between 250 and 350 ohms. If this sensor is not sending a correct signal when cold, the air/fuel ratio could again be inappropriate.

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Saumil S. Patel