Sheesh, no.
Scan, seriously.
A brief explanation of the problem:
Your Microcontroller in the Climate unit has several inputs. Desired_temp, present_temp, engine_coolant_temp, outside_temp, sun_status, eco, footwell_out_temp, screen_out_temp, vent_out_temp, central_flap_position, temp_flap_position, recirc_flap_position, among others.
If *any* of those position readings are inconsistent or implausible, your desired_temp will not happen.
The position readings are taken by the relative position of the wiper of a potentiometer, which is moved as the flap moves. Now what is plausible and what is not has been seen elsewhere to be virtually impossible to detect with a meter. I have no idea of the frequency with which the position information is requested (though I suspect it's of the order of several Hz). If I remember correctly, it's 300 Ohm pots or so.
Seriously, don't waste time. Get a scan completed, work out which pot is at fault and replace the flap. All the motors are the same, it just has a different tongue on it; a temporary respite *may* be gained by exercising the flaps through (in VCDS, go through to the climate control unit, and hit 000 in measuring block 1). It is probably easier if you take the dash out, but it's not really necessary.
If I remember correctly, there's the temperature flap, the recirc flap, the central flap (for up, down, vents) and there might be one more. Normally it's the temperature flap which is dodgy, though the central one also goes over time.
If the Aircon is not gassed properly, you'll also see that in VCDS... so scan.
As far as the multimeter is concerned - the A2 is already the generation where you're not going to get far without an osci and a deb u g g e r for the messages.
- Bret