Originally Posted by JaXeN

In my experience, the outside temp sensor for the display on the dash and the outside temp sensor for the climate control are completely independent of each other.

Learned this the hard way with my last Audi when I had symptoms similar to yours.
In my case though, setting the CC controls to MIN or MAX would give me cold or hot air respectively.... Anything in-between would yield results similar to what you're experiencing.

With the cable and software, you should be able to determine fairly quickly what's amiss with your system.