The temperature control does not work properly.

I had this problem. You can google search for a youtube video about how to clean the heater control valve. My dealer wouldn't do it but it only takes ten minutes to do yourself. The valve stems get covered with sludge over time and then they can get stuck open. The only tool you need is a torx screwdriver and some cleaner and a cloth. Simplified steps: 1) make sure your car is cold and on a level surface 2) open hood 3) the heater control valve is hidden under the plastic cover close to the windshield/firewall. Pull off the rubber strip that goes lengthwise across the engine compartment about a foot away from the firewall and then pull off the plastic covering 4) locate the HCV. Its in the centre, galvanized metal with two cylinders 5) have a plastic bin ready to collect parts as you disassemble 6) take your time so you don't loose parts 7) disconnect the power supply to the HCV at the back. This is for safety. The clip is a bit finicky 8) using the torx screwdriver, loosen each and then remove (don't use a power screwdriver this junk is made in france)the screws 9) remove the two caps slowly as the inside parts may want to come along 10) remove the two plungers. You should notice sludge buildup. It doesn't take much. Watch so the springs don't come out. If they do that's okay just put it back together properly. 11) use a non scratchy cloth and some cleaner/polisher that's non abrasive to clean the sludge off 12) put if all back together and be sure not to overtourque the screws I've done this twice now. It seems to me that antifreeze and engine gunk collects on this items

I have never owned an Audi, but I have had this problem with a Volvo I owned. It may be that your dash vents as well as the heater actuator is controlled by vacuum lines from the the engine. If there is a vacuum leak in any of these lines then these kinds of problems can occur. Check all of the vacuum lines under the hood in the engine compartment (there should be a sticker with a drawing of the routing of the vacuum lines somewhere in the engine compartment,or it will be available online) and make sure they are all tight; and examine them for cracks. Replacement vacuum hose is inexpensive and if you are willing to take the time to examine all of the hose locations, this may fix the issue. If this is the issue, you may have noticed a decrease in mpg also, as correct engine vacuum is critical for the proper operation of the fuel injection system. If all of the under hood vacuum lines are good, then there is probably a leak or disconnect of a vacuum line under the dash that controls the vent actuators or a problem with the mechanism that controls the vents opening and closing. A good foreign car mechanic should be able to determine the cause of this issue; however, if they have to get under the dash to fix it, it may drive up the labor cost.