It is has many names, auxilary electric fan, condenser fan, AC fan. Basically its in front of the radiator and it helps to keep the condensor cool by drawing heat away from it. Without it running, the AC is very inefficient especially in hot weather like over 85 F. I know the AUX fan is controlled by the FSR and other things, which is why I will replace the FSR first. But i have yet to find a post about an aux fan coming back to life after replacing the FSR. most users experienced erratic fan behavior, but mine simply does not go on anymore.

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2005 BMW X5 3.0i
2013 BMW M3 Competition