Does this car have a mechanical or electronic fuel injection system ? I am not very familiar with this car but if it were happening to my 87, 260E, these are the things I would check.

Coolant temp sensor that sends engine temp to the fuel injection computer and the ignition control unit. On my 260E, the sensor has 2.5 to 3.5K resistance when engine is cold and then the resistance decreases to between 250 and 350 ohms when the engine reaches 80 deg-c

vaccum and fuel leaks

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Saumil S. Patel