To me it sounds like you re talking about the electric auxilary fan.
Bmw e46 auxiliary fan relay location.
There s a clutched fan spins off the water pump belt driven behind the radiator standing in front of the car facing it and there is also an electric one in front of the radiator.
If the fuse is not blown the most likely fault is the final stage unit or the fan motor.
On all bmw models up through the late 90s the auxiliary or main fan is controlled by one or two thermostatic switches that are mounted into the radiator side or bottom tanks.
If the fan runs erratically continuously with the key removed from the ignition or not at all and the fuse is good the speed controller has.
The fan is mounted between the radiator and the engine and is the main engine cooling fan.
This is the electrical fuse and relay box under the plastic cover in the passenger side rear of the engine bay.
Various relays in the bmw e46 the first set of relays is located behind the glovebox.
Bmw models that do have an engine driven fan will also have an electric fan mounted in front of the radiator known as the auxiliary cooling fan.
This relay location requires that the glovebox be removed for access.
There is no engine driven mechanical fan.
For cars from 1999 model year without headlight washers.
For the bmw 3 e46 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 model year.
While troubleshooting the e46 aux fan is outside the scope of this document i ll point out that the e46 design replaced the individual relays with a speed controller integrated with the fan.
The bentley repair manual shows the location on page ecl 20.