These cars use a pair of negative temperature coefficient thermistors to sense the outside temperature. One of them is located in the plenum where the climate control air intake is located (under the hood on the passenger side) and the other is attached to grille next to the driver's side headlight. Both thermistors are identical and are 1000 ohms at 25 deg C. They have an R value of 9.10 and can be purchased from Digikey Corp. in Thief River Falls, MN for approximately $2 each. The part number is KC016N-ND. This is actually a Keystone Thermometrics part. The K.T. Eng. P/N is RL2004-582-97-D1. The AC head unit reads both sensors, then displays the one that senses the lower of the two temperatures. This is done to prevent the display of an artificially high temperature due to engine or sun heating. The temp may still be a little high, but at least it would be the lower of the two. The problem is when one of these sensors goes bad, it typically increases in resistance. That means that your temp display will show low. If the climate control thinks the outside temp is really low, you'll always get heat from the vents at all settings, except "LO".
The display will operate with only one sensor, so you can do one of two things. Best choice is to check the resistance of each sensor at approximately 25 C and see which one is reading high, then replace it. Second approach is to unplug each sensor separately and see which one makes the temp read correctly (assuming you haven't been parked in the bright sun or just run the car and the engine is hot).
To replace the thermistor, you will need to remove the bad assembly, then remove the plastic tip from the holder. The original thermistor is soldered to the two wires and fits into a plastic tube. The new one is just slightly larger, so you will need to insert a screwdriver into the plastic tube and enlarge it approximately 0.02 -- 0.04 inches. Audi would be happy to sell you a replacement, however, they list for approximately $100.
