HI, have you tried the Idle control valve? This is a very common fault on Audi's! I had the same problem with mine recently, and was able to get away with cleaning it out with carb cleaner. If you contact
martyn@partsforaudi.info he will be able to advise on price and availability for a replacement. He will also send you diagrams and part no.s to help you locate it. If you're lucky, you may get away with a good clean. Good luck and let us know how you got on!