My problem is the same but in the winter the problem does not exist only in the summer tried a new mass air sensor but no change fuel pressure is ok have not checkt the fuel volume becuse I don't now where I jump so the fuel pumps run with ignition on.
Fuel pumps are not old in my car the car is 1994 E320.

There is no code thinking of the coil but my first thought was mass air sensor since the problem seems to be temperature sensitive.