After I shut the car down I hear a noise from the grill that sounds like a fan motor or a water pump that continues to cycle. I've let it go for as long as five minutes, but it does not automatically shut off. The only way I can get the noise to stop is to restart the car and shut it down again.
Will this pump/fan automatically shut down eventually or will it run on until the battery is completely drained?
I didn't look, but if its like most euro cars it has a pump that continues to circulate coolant after shutdown to keep cooling the engine. It may be 10-15 minutes before it stops. The fan may also run. If your battery hasn't gone dead yet, its probably fine. Restarting the car circulates a little bit of coolant and tricks the sensors that run that feature.
My 2001 TT 225 does this also, there is a pump for coolant and one that runs oil to the turbo for the same cooling reasons, if you idle it for a few after a hard run before shutdown it will shut off faster.
There is no turbo oil pump. The turbo is both liquid and oil cooled. What your are hearing is the auxiliary coolant pump and electric radiator fan that continues to cycle coolant through your engine and turbo to avoid hot spots and turbo cooking. Thus, eliminating the need for a turbo timer or cool down idle. However, 15 minutes is too long for this system to be active. What is the amount of time it stays on?