E28 535is running problem - need help

This is a e28 manual 535is in great condition well within regular major services. I have an idea of what is wrong but would really like some other opinions. Here are the symptoms:

In warm weather: car will start, no problem, idle no problem, just off idel the car will die occasionally with a pop from the exhaust pipe. Once the car is warm the car will not start-crank fine with lots of power from battery but will not start.

In cold weather: car starts great, drives just fine but when RPM's get above about 3k it starts to knock or make a missing sound as though it is bouncing on the rev limiter which it is obviously not.

Symptom came on rather sudden and it is an extra car so it's not getting driven very often and now not at all. Now that cold weather has arrived I can drive the car down the street no problem but forget about punching it.

Thanks for all opinions.

It may be that the coolant temp sensor has gone open circuit. The ECU would then act like the engine is stone cold, so cold starts would be OK but during a warm start there would be too much fuel. My 528 had this problem when I bought it, including not being able to rev past about 3K RPM. Have you noticed black smoke out the exhaust?

It's easy to check with an ohm meter, it should read roughly 2K at ambient temperature. Resistance decreases as it warms up.

Airboot?????

airflow meter and intake manifold.