I know this is an older thread, not too sure anyone is still reading through it...My '04 A6 2.7 just started a similar issue this morning - 45k miles. You could always hear the cooling fan whirring down after I shut the motor off, but this morning it came on quite loudly and never shut off. A/C on or off. About 55 degrees F out and raining. Never had any issues with overheating, etc. including today. If anyone is still reading through here, is this the thermostat?

 

Wrobo
A coil went bad on my 2000 A8 140k. AutoZone carries OEM coils for $30 each. They are replaced in 10 mins with 2 x10mm bolts after removing the plastic shrouds. You can easily self-diagnose by running motor and unclipping coil connectors one by one... the one with no change in engine sound is the bad coil. My Check Engine light went out by itself after I changed the coil. I keep a spare coil in the trunk now! I have a noisy aux fan motor too, but in my case need a new assembly. OEM assemblies available online for $60. Does anyone know if the bumper must come off to change the aux fan assembly? Or it is all done under the hood?

 

I recently found out there is a recall on all coils for A8, they will perform the service, replacing all 8 coils for free as part of the recall.
Also good for VW Phaeton 2004, and VW Touareg 2004.
Hope this helps avoid expenses.

 

I am tired of fan keep running after I shut off the car. 3 Miles run up and down in 20 degree outside and this happened. As soon as I get back in the car start and shut it off, the fan shuts off too. I need this problem to be resolved.