The blower resistor regulates current as needed to control the speed of the climate control fan. The fan speed switch on the dashboard selects the resistor's mode. If your BMW Z3's climate control only functions when the fan speed is set to the "high" setting, which bypasses the resistor all together, then your blower motor resistor is likely defective. Replacing the resistor pack with a new one will solve this problem.
Remove the two screws holding the trim panel that's located directly below the steering wheel. Unscrew the Phillips screws using a screwdriver and pull the panel away from the dash.
Remove the metal shield that covers the under-dash components. Use a socket wrench with a 10mm socket to take out the 3 bolts on the shield, then pull it out.
Pull out the plastic duct that exhausts air at the driver's feet. It's not bolted in place, so simply wiggle it with your hands until it is free to remove. The blower resistor is now exposed.
Unscrew the screws running through the resistor pack using a size T-20 Torx screwdriver. The resistor pack is the square black box that is wrapped in aluminium on its sides. Pull the pack out of its socket.
Install the new resistor pack by reversing the process used to remove the old one. Gently slide the pins on the bottom of the pack into the socket. It will only go in one direction. Do not force it into position. If it is difficult to install, rotate it to a different position and try again. Replace the T-20 Torx screws.
Test the system to make sure it is functioning properly, then replace the dash panels by reversing the procedure used to remove them.
When obtaining a replacement resistor, be aware that your BMW parts dealer may also refer to the part as the "Final Stage Unit" or the "Blower Resistor Pack."