Sunday I had a problem that the aux fan stopped completely on my E32 750iL. Temperature here was 38 degree C, had wife and son with his wife and 8 month old baby in the car, on the highway traffic jam and the needle went up to 3/4, but not higher as I have a good working visco clutch, but aircon got warmer, probably due to icing as as the aux fan was not cooling. Made it home, when no traffic jam temp needle almost was in normal position.
Today I continued to check based on the info from Gale's site and the ETM. Replaced all related fuses just to make sure all are o.k., changed low and high speed relay, jumpered the plug on right side radiator, no change. Then I removed the bumper and the kidney grill, unplugged the plug on the aux fan and connected a spare aux fan, that worked, but with loud noise. Because the magnets inside aux fan motor are lose as often happens. Will repair that one next weekend with wrenching buddy Hairywithit and re-glue the magnets, so I have a spare aux fan. Disconnected aux fan again, measured with multimeter, all o.k., installed aux (about 8 years old) fan spins easy, so no problem with magnets.

Then I sprayed contact spray into plug of aux fan on aux fan and the connecting plug, O.K., fan runs on low and high speed again. Just oxidation of the pin contacts. The plug is just behind the kidney grill and rain will come there. I forgot, maybe better I additionally use some good tape to seal the complete plug portion from rain. So just another case of bad contacts/oxidization which caused a problem.
2 years ago I found oxidation on the spades of the high speed relay, also causing malfunction of the aux fan.

How to test:
http://www.nmia.com/~dgnrg/page_2.htm
http://www.bmw4life.com/repairs.htm