Hi, I just went through this about 6 weeks ago. The following info applies to my 91 740. I'm not sure how your car will differ. Here's what I've learned...

1)To test the fan circuit which includes the relay, trip the a/c temp sensor which is a 2 pole connector plugging into the back of the passenger side of the radiator. Unplug the connector and join the 2 terminals of the connector wire (not on the rad) with a wire. The electric fan will come on if the circuit is good and the fan motor is working and not seized. If so, the coolant temp sensor isn't working, or everything is fine but your coolant just wasn't hot enough yet.

If it still doesn't work, the relay for the electric fan might be bad. On mine it is clipped on the front of the coolant reservoir on the passenger side.It is the identical to the radio interference suppression relay on the driver's side engine compartment and the two can be swapped for diagnostic purposes.

2) replace the fan relay with the RIS relay and try the test from 1) again. IF the fan works, get a new relay or look in the FAQ section for how to re-solder them.

3) If it still doesn't work, the fan motor might be shot. Find the 2 pole connector behind the grill on the passenger side that goes to the fan. Test the fan motor directly by putting 12V to the connector.

If the fan works, you may have a bad connection "upstream" of the connector and will have to find it with continuity or voltage checks with a multimeter.

If it still doesn't work, the electical connection right at the motor or the motor itself must be shot and needs replacing.

Keep in mind, you can have more than one problem at a time. In my car, I had a bad relay, and fan blade that was warped AND a defective climate control unit. It all works now after replacing the relay and fixing the other two, but I trouble shooted it as above, thanks to this board.

Good luck.