LOL! I guess we are in the same boat!
Yes, when I took the AC unit out I realized there is only one fan and it's on the left side, and that explains why only the left vent collects dust! But, I am not sure the fan is what regulates the temperature. (What does the fan do? Do you know?) There is this shinny glass-like dot on the right "vent" and it might be a sensor! Do you happen to know what it is? If you look at the image above, it is located in the lower right corner of the bottom groove of the right vent.
And I agree with you: if something breaks, I try to fix it my way by improving on it. Especially the E39 cupholders which have so many design flaws!
1) They are shallow so any half filled cup tips over.
2) They are flimsy so they don't hold cups in place and break easily.
3) The cups block access to the AC controls.
4) Drink temperatures affect the climate control.
^BMW really dropped the ball when it came to the cupholders (even though I love the rest of the car)!