Problem Description and Possible Solution
The blower final stage fan resistor is known to fail. Symptoms are the heater fan speed varies regardless of the setting, the fan will not turn off when the car is switched off, or the fan will not switch on at all.
Average mileage: 110,600 (10,009–202,000)
20 people reported this problem
Blower motor continues to run even with the ignition off, and key fully removed. (it's really freaky).
Found parts online $60, readily available. (My local dealer, BMW Concord, CA. quoted me $193 for the part), found video on YouTube how to replace, took about 20 minutes.