assuming the a/c systems is the same as the one in the F10, I too also found the fan speed button logic a little odd , I was coming from a E39 where when you pressed Auto, everything was automatic including the fan speed.
So when I picked up my F10 (on a resoanbly warm day) I was surprised that he fan speed was low despite setting a low temperature and 'auto'.
WHen teh car was delivered, the fan speed was set to its minumum speed.
Looking atthe manual, and its not clear you do need to set the speed and I've set it to the middle setting and its been ok from that point on.
I'm not sure why BMW have put this logic in and its not obivious to me. I assume if auto was selected, it would handle everthing. The only expcetion of course being the ratio of warm or cold air to the vents on the dashboard which you select via the dial. In general , I have it set to the middle point dueing the winder and at cold during the summer.
AS otehr have also mentioned, if you have conigured eco pro to reign back on the a/c to aid fuel consumption it might be worth undoing that. (I have)
And also to make sure air recircualtion is not set. (I have mine set to automatic - where it supposed to detect bad odours outside the car and switch to recirculate automatically)
All of the above assumes that there is no underlying problem with your car. If its pumping out cold air that suggests you don't have a leak of gas.