Not that this is your issue, but some good things to check over. Inspect your cabin air filter and make sure it looks good/clean. Check your coolant level. Also, have you had the system recharged at all? I'd do this first before diving into it more. I have seen more than a few times that a low charge will mess give off warm on one side and cold on the other symptoms. It is possible that the heat flap in the HVAC unit is stuck in the heat position. The HVAC Temperature Control Actuator is what moves the flap/valve from heat to AC ducting. I've posted some info from other threads where people described your issue below. I have also seen a failed compressor cause an issue similar to yours as well, they described a noise/click from it.
Quote:
Here is some more information that may be useful to diagnose the automatic A/C systems that BMW refers to as IHKA.
There is an on board diagnostic built into these systems, what follows is the procedure on how to access the on board diagnostics: The system has three modes. MODE1 - Shows any fault codes stored in the system. MODE2 - performs a calibration run of the doors that control mix and air distribution. MODE3 - provides for manual operation of the features.
Put the ignition in position 2 then press the OFF and blower PLUS buttons together for two seconds, the display will show a single streamer to represent MODE1. Each time the OFF button is pressed a different mode is displayed; to access any mode the AUTO button is pressed. In MODE2 the servo motors can be heard cycling from open to close position, this movement is detected by potentiometers built into the motor assembly. assuming the doors are still coupled to the motor shaft then the motors and doors will cycle and not give any errors, if the doors are not coupled to the servo shaft the system has no way of knowing and will cycle the motor end to end as reported by the sensor in the motor and everything will appear to be OK. Otherwise MODE1 will give any errors the system detects. There are 10 possible codes. I will post if anyone is interested.
Code Description
01 Solar Sensor Fault
02 Interior Temp Sensor Fault
03 Heater Core Temp Sensor Fault
04 Air distribution servomotor feedback fault
05 Blend Flap Servomotor feedback fault
06 Blower switch minus fault
07 Blower switch plus fault
08 Interior sensor fan fault
09 Air distribution servomotor fault
10 Blend flap servomotor fault
The display will show either CA=Calibration Active; CC=Calibration Complete or FF=Fault.
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Hope this info helps and report back with your findings.