Various relays in the bmw e46 the first set of relays is located behind the glovebox.
Bmw e46 cooling fan relay location.
If the fuse is not blown the most likely fault is the final stage unit or the fan motor.
This is the electrical fuse and relay box under the plastic cover in the passenger side rear of the engine bay.
These cooling fans rely upon electric motor and they typically have a moderate to high slow draw which means that they are commonly controlled with a relay that relay controls the fans for the engine.
The bentley repair manual shows the location on page ecl 20.
If the fuse is blown replace it and see what happens.
Almost all modern vehicles rely upon electric cooling fans to pull air through the vehicle radiator to keep the engine cool.
For cars from 1999 model year without headlight washers.
This relay location requires that the glovebox be removed for access.