over heating issue
If the coolant really is overheating (boiling in the reservoir tank) just check:
1. the feedback line to the plastic tank is not blocked (got caught on that one before!),
2. you have bled the air out of the system when refilling the coolant by, (a) bleed screw on the metal line next to the valve cover and (b) a bleed hole in the heater hose near the fire wall, - that one won't bleed off until the thermostat opens, so you release the hose clamp, pull the heater hose back about 1/2 inch so the little bleed hole which is marked on the heater hose is exposed to the coolant but not all the way off. Turn the heater to full heat, and run the engine for about 2 or 3 minutes, the thermostat will open allowing the coolant flow into the heater core, the air will bleed out and you should get a little water fountain out of the bleed hole. Push the heater hose back on and clamp up.
If you don't get a little water fountain or if the above does not solve your problem, then I agree with lyleswk to focus on the water pump.
Unfortunately to get at it you have to drop the front off the car. Its actually not as big a job as you may think as the Audi is designed to do this for major servicing, belt replacement etc If you just did the thermostat housing, then you are capable for this one.
The pump is actually quite cheap to buy, and easy to install. The trap is when you do this you think, hey why I'm here, i'll replace the timing belt, tensioners, etc etc but thats your call how much you want to replace.
these are just my thoughts someone else may have a better way of testing the water pump is actually pumping.





