Yes, if the pressure drops due to a leak somewhere, the car will have warm start problem.

Another item that can cause this problem is the coolant temperature sensor also called fuel injection temperature sensor (atleast on my 87 260E). This sensor informs the computer about the engine's temp and the computer adjusts the air/fuel ratio accordingly. On my 260E, this is the last sensor (closest to the windshield) on the air intake side. It has two terminals. You should have a high resistance (2.5K to 3.5K) when cold (20 deg-C) and a low resistance (250 - 350 ohm) when the engine temp is 80 deg-c. The exact numbers may be different on your car BUT the resistance should reduce by approx a factor of 8 to 10 when the engine temp changes from 20 to 80 deg-C.

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Saumil S. Patel