If all of your fans are operational - your thermostat is stuck partially opened.
But IMHO - you have a fan that is malfunctioning or even- 2 fans.

 

the overheating thing isnt necessarily a bad thing man, my 01 a6 2.7t quattro with 224,500 miles does the same thing, the ac still stays cold though....if it gets to a level where its getting too hot the car will itself shut off the ac and blow hot air and you'll get a warning on the dash.....keep in mind our cars arent exactly new anymore. another thing that might help is to have you cooling system flushed,, as the coolant runs through the system over the years the aluminum hoses have bits that come off and clog some of the arteries.....have it flushed well and have all the gunk if any removed. it helped me a great deal as i i suffered the same thing you said...these cars are really well built. audi arent lying when they say they are the truth inengineering. good luck

 

I had the same overheating problem. It was AC Condenser Fan.Thats the passenger side fan. Replaced it never had a problem again.