I need another forum member with the same problem to try something on their Z4. I have gotten the noise to stop using this technique. Not a fix but if others have the same result it might help finding the fix.
If I put my blower on and make sure recirculation mode is off(fresh air mode on) and turn off the vehicle, when I start up again(after a 15-20 minute wait) the noise is gone. What is happening is that by leaving the car in fresh air mode, the fresh air flap stays open, and by default, that flap is immediately closed when restarting the car. According to the OP of this thread, there is some kind of spring that should pull that flap shut, but that doesn't seem to be the case on my car.
So the sequence is, turn on car, using manual mode for the air system(if you have automatic) turn on the blower, and be sure that the "recirculation" light is not lit. Shut the car off in this position, wait about 60 seconds, then turn the blower off. Wait 20 minutes and put key in 2nd position to see if the noise is still there. Tx in advance.