2002 BMW 325 blower motor

Check the blower relay K4 and blower motor M30 on the air conditioning unit

The E-46 body style has a potted semi-conductor device called a final stage that controls the fan speed and it is probably the culprit here. The fan motor is not the first thing to blame here. The final stage is accessed through the passenger side (right side) foot well area, take the glove box out to get to it. It is held in with a Torx screw. The part can be bought from Realoem.com and is listed under the heating and A/C section. Once you get the g-box out you will see the wiring connector going to the unit and having the replacement in hand will aid in its recognition. It is a very high failure rate.