It could be a faulty coolant temperature sensor (also called fuel injection sensor). The signal from this sensor informs the fuel computer about the temp of the engine. The computer can then adjust the mixture accordingly. In my 87, 260E (and perhaps in youir car too), it is the last sensor on the engine, towards the windshield. Should have two terminals. Measure the resistance across the terminals. When the engine is cold, you should get between 2.5 to 3.5Kilo ohms and when the engine is warm (80 degC), the resistance should drop to 250-350 ohms. The exact values may vary, but the resistance should drop by a factor of 8 to 10 when the temp changes from 20 degC to 80 degC. Let us know what you find. Also check the wires on the connector for any breaks.
Have you changed the OVP relay anytime in the near past ? Take it out and clean its terminals and insert it back, make sure the contacts between the relay terminals and the socket terminals are properly made, the connector is not very stable.
Dont worry about the fuel distributor yet, too early to point a finger at that really costly and a very robust part. Fuel distributor also can be roughly tested when needed.
Linear Mode
