Had the same problem with my 2000 A6, turned out to be the climate control module. bought a used one on Ebay from LKQ very reasonably priced and it works fine.........

 

Classic bad thermostat sign...

 

Thank you! i thought it would be that also, but i think the car has two issues. one that the thermostat might be bad but the second is that it blows cold air inside when the engine temp is at normal. i have noticed though that when i push the gas pedal down and get it up to 3-4thousand rpms, the air starts to come out very hot from the blower. So i understood that it blows hot air only at high RPMs. Clogged heating core maybe? air inside the heating core maybe? bad water pump maybe? what do you think? any help?

 

Seems like its time to do the timing service.. Water pump, t-stat for the heat/cooling and belts, tensioners since your there...