If your car hasn't been altered from original you have TWO fans. One electric in front of the radiator, and one belt-driven through a viscous clutch mounted on the water pump. What you're describing sounds like you have no belt driven fan, the absence of which is sometimes called a "FDM", or fan delete mod. When you drive, enough air passes through the radiator to cool the engine. When you stop and let the car idle, the belt-driven fan is supposed to pull air through the radiator to cool it when there is no airflow from the car moving forward. The electric fan in front of the radiator is there as an auxiliary air mover to push cooling air through, primarily when using the air conditioner. It's function is also to add cooling air when the car is stopped and the ambient air temperature is too high for the clutched fan to cool the engine by itself. It appears your electric fan is DOA, BUT the engine's belt driven fan should have sufficient cooling to keep the engine from overheating almost all the time.
#1: verify you have or do not have a fan behind the radiator. If you don't, get one, along with the clutch, because it is your PRIMARY air mover.
#2: IF you have the belt-driven fan, the clutch has failed. Replace it.
#3: read the stickies (permanent at-the-top-of-the-forum threads) particularly those concerning cooling system maintenance. The ENTIRE cooling system needs to be replaced every 70,000 miles or so. If yours hasn't been replaced in that time period, or you don't know when it was last replaced, do it. Don't argue that it "looks fine", just do it. BMWs do not tolerate overheating, period.
#4 Welcome to the fest!