clearly temperature related...sounds like your mixture goes bad when it warms which is generally a sign of a failing DME temp sensor. Since you did replace your fuel pump and suspect it was bad...you can put an in-line fuel pressure gauge in and see if your pressure changes as the car warms...unlikely though. Check the connector to the DME temp sensor...make sure it isn't corroded...sensor can be good but connection maybe bad dramatically increasing resistance. I would recheck your new sensor with a multimeter to determine diff temps versus resistance per Bentley as well. If that all checks, check/clean the AFM...run some simple flap versus output checks per Bentley...to make sure there is an approx. correlation...could be the air temp sensor in the AFM also...though they rarely fail. Lastly, most likely a failing O2 sensor. The O2 sensors on these cars are heated and therefore don't talk to the DME when the engine is just started and running cold. As the engine warms, the DME does glean input from the 02 sensor and may be getting bad info thereby adjusting air/fuel incorrectly. Sounds as though you have an early E-32 with 1.1 Motronic which is not suspectible to the stomp test as with later E-32's.
Motronic 1.1 can still be analyzed with a Bentley manual however. My hunch is it is one of the above engine management sensors that is creating your warm driveability problems.
HTH,
George
90 735iL/149k...also own an E-32