I can't comment on the TDi question, but this happened on my 1.6FSi Sport around 2 years ago - at first I couldn't even see where the water was leaking from as pipe is so well hidden..
Anyway, Audi book price at the time was (I'm 99% sure about this) £350 which considering the aggravation involved seem good value - I took the quote to my local Audi/VW independent and they said they would do it for £250, so I went with them - the guys (as you need two people to do this properly as one end goes into the back of the water pump and the other the thermostat housing) said it was a Bas****d of a job and would think twice about doing another one without charging a lot lot more.
Everything was good for about a year, then the upper heater pipe (which had not been re-positioned back to where it was following them dismantling / re assembling the pipework to get at the thermostat housing - I hadn't spotted this) rubbed through against the inlet manifold. Make totally sure this doesn't happen to you! as the heater pipes are yet another Bas****d job to get at.....
I replaced both when I did the engine/gearbox swap last week and noticed the design has changed - they now bend further away for the manifold, so Audi must have realised this was common point of failure.
Brett kindly pointed me to the German A2 site where there is a good write up (in German) with pictures where the pipe was replaced from below following the Oil separator being removed.
HTH
