Starting Problems

Hi,
I am having problems when starting my 87 528e. When the outside temprature is cooler, the car starts fairly quickly and without problems. But if the temperature warms up outside, it is really hard to start. I have to crank for about a minute before it kicks over. It acts like it is not getting any fuel, but then when it finally does start, it runs fine. If I run the car and don't wait too long after stopping, to restart it, it works fine. But if I wait about 2 or more hours, then it has trouble again.

Any ideas would be appreciated.

I could replaced the fuel pump for $200 but I fixed the problem by putting in the fix from BMW for about $3.50,
part # "16 14 9 068 988"

Now the engine starts on first turn, hot or cold, overnight or after
standing for a while.

Diagnosis:

The check valve in the main fuel pump was leaking allowing the fuel injector rail residual pressure to bleed off resulting in formation of a huge fuel vapor bubble in the fuel rail and back down the fuel line toward the pump.

The extra cranking time was needed by the fuel pump to recompress and
eliminate the fuel vapor bubble in the line and repressurize the fuel injector rail.

Installation can be anywhere in the fuel pressure line but next to the main pressure pump is best.

It is a two screw clamp job.

Later,

I am having some problems locating that part number. Can you tell me any more about it, or perhaps where I can get the part. I appreciate the information.
Thanks