Climatronic Error Code 313: Troubleshooting Guide

Hello,

While this might be a bit off-topic, I hope someone here knows the answer.
I'm having a problem with the outside temperature display on my Audi/Volkswagen Passat. It occasionally shows a temperature that is too low. Usually, after a few minutes, the display corrects itself and shows the correct value.
Okay, I just replaced the external temperature sensor [1], but the symptoms have only changed in that it still occasionally displays too low a temperature, but the value no longer increases; instead, it immediately jumps to the correct temperature.
Does anyone have anything to say about this?

Thank you in advance.
Ronny.

[1] The prices at VW are completely crazy. An outside temperature sensor for my 1998 Passat 3B costs about 54 EUR. I bought one for a 2001 3BG, and it only costs 2.48 EUR! Okay, for the 1998 model, you get the sensor with the cable, but for the 2001 model, you only get the sensor. But that's not a big deal; the soldering iron is your friend.
I find it quite outrageous to charge 52 euros for a piece of cable that's only half a meter long.