The thermostat will be where the radiator hose attaches to the engine block. You can't see it without the radiator hose off. A quick internet search tells me that your Audi's thermostat might be near the lower radiator hose, but I've seen them on other cars on the upper hose.

Drain your radiator and take off the lower hose. Keep that bucket ready, because the engine block will drain when you take the hose and 'stat off. Once you remove the hose you should see the thermostat in the center of the tube you removed the hose from. It's that brass thing in there. The metal tube that the hose mounts to should have a couple of bolts holding it on. Remove the bolts, give the piece a smack to knock it loose, and pull out the thermostat. Make sure you clean everything up and put a new gasket on before you close it up again.