When I restart the engine without letting it fully cool down, e.g. after half an hour, the idle is so rough that the engine feels like it could stall at any moment. Also, depressing the throttle will then at best result in a hesitant acceleration, at worst in a DEceleration.

Have any of you experienced these symptoms, and if so what were the causes?

Thanks!

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1991 W126 300SE (M103)
1995 W124 E320 Wagon (M104)

Be sure to check all vacuum lines. I had a problem similar to yours and it was a vacuum line under the air cleaner.