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.
Car Problem Reports
BMW 528i Blower Final Stage Fan Resistor May Fail
BMW 528i Problem
Average Mileage: 100,930 mi (70,000 mi - 133,720 mi)
Visitor, 2000 BMW 528i
Fan flows at full blast. Dealer fix under warranty
Visitor, 1997 BMW 528i, 80,000 mi
Blower motor worked erratically, then gave up entirely. BMW dealer mechanic said this is common for the vintage.
blower fan speed increases and decreases eratically. went away after the internal resistor was replaced.
Same symptoms as described. Replaced FSU/Blower Motor Resistor and problem seems to be solved. Made the repair myself. Part cost $67 at an import car parts store. Net savings of $183 from dealer costs (labor & parts).