Quick and easy way to test whether the aux fan is dead or not-

Unplug the A/C high pressure switch.
Start the car with the A/C switched on, the Aux fan should run full noise (fail safe) straight away.

If it does not - time for new Aux fan.

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2003 E53 3.0
2001 E46 330ci Msport
2001 E46 325i Touring wagon