I don't have an S3, I have a 2.0 tfsi A3 (AXX) but I believe they're fairly similar engines unless I'm mistaken?
The thermostat is sat behind the intake manifold and you can see it after removing the alternator and alternator bracket. From here, you can just about get some tools in there to get clips off the pipes and the bolt out of the middle one that I believe goes to the heater matrix. Once the clips are moved out the way, you'll spend the rest of your time trying to pull the pipes off, move the pipes out the way and pull the stat out.
I'm not ashamed to say it took me an hour to actually get to it and then the whole day with 5 friends to get the thing out.
If I had to do it again, I would just pay someone else to go through the ordeal...