I need a good problem solver. I have a pretty good idea what might be wrong with my car, but I'd certainly like to hear from bmw community.

Signs:

Car overheates when idle(maybe after 15 minutes of idle).
Never overheates when driving or on stop signs.
When it starts to overheat I turn on heating and it cools down.
When it starts to overheat I turn on air conditioning and it cools down.
When it starts to overheat I press on the accelerator and keep it at 2500 rpm and usually cools down (not all the time, but most of the time).
No coolant leaking or coolant loss.
I didnt' do the compresion test but I bought that Napa combustion test kit that checks if there are exaust gases in coolant and it was clear (I did it few times).
I tried to stop fan with paper when it was very hot and I was able to do it without too much pressure. When I try to turn it when engine is cold there is some force stoping it but not a strong one, so it doesnt move freely on shaft, just a few rotations and then it stops.
My auxiliary fan works (I tested it with 12DC) but never turns on (even with AC on). I still think it should turn on when engine overheats (I wish I could get to that fuse #75 to check if it was blown).

My final diagnosis is Fan Clutch.
Let me hear your opinions??

sounds good

The electric fan should come on period when the ac is on or the engine runs hot. Replace the fan sensor. Now your going to ask where it is. If your mechanically knowlegable, buy a manual to learn your engine. If you refuse to buy a manual, take it to a shop. You will end up burning up your engine trying to keep it cool.