BMW 328i AC Not Cooling

Would need to know what make , model an year the vehicle is ?

check the blower motor resister. This protects the fans and blower motor. Before fans come on the thermostat has to open at 192 degrees

A/c compressor works fine and the blower motor works and shutdown right? it is the problem with the blower resistor or with blower motor relay. try to direct the resistor irrespective of the speed. hope the problem may be solved.

It may be the blower motor, or it may be the blower resistor. Check for power at the blower motor. If power present with system on and blower has good ground, motor bad. If no power check blower resistor in air box prior to blower motor. If power on input side but nothing coming out to blower change resistor.

Check fuse supplying fan is not blown,
Check blower control switch is operating OK,
Check relay controlling fan is operating OK,
Check variable speed resistor pack is not faulty (the resistor pack is usually located in the blower ducting, in the blower airflow),
Check blower motor ground connection is not missing.

You have clean the blower unit , may be its dirty then . and then check the blower resistor unit for malfunction.

The resistors are in circuit only on the lower fan speed settings.
On the highest speed setting, power is switched directly to the fan motor.
Check fan power supply fuses,
Check power is available to the fan when high speed selected.
If all above OK, apply power directly to the motor to verify fan motor runs- if it doesn't the motor may need replacement/repair.

blower motor or resistor or the blower motor control switch.

it's either a fuse or it's a bad blower motor, it could be a bad blower motor resistor but usually you'll get either high or low only, so if you have nothing on any speed, high low etc, and all the fuses are ok chances are it's your blower motor.

well you need more detail to know, start by check your fuses