The thermostat housing on the Tdi is different to those on the 1.4 and 1.6 petrol engines ; simpler pipework locally for one thing. Two bolts to take it off, but it is in a swine of a location adjacent to the alternator. The housing is an angled plastic moulding that bolts onto the lower engine block. Taking it off when it's not been done recently will snap two plastic fingers off that hold the thermostat in place when being installed the 'official' way (thermostat twisted into housing, housing secured onto engine block). When the housing comes off (losing the fingers in the process), the thermostat stays in the block held in place with the o-ring in front. A small flat-blade screwdriver can release the o-ring, then you can pull the thermostat out and replace, but a fair amount of coolant will be lost in this process. G13 (bright pink) coolant at the right concentration is essential - but also make sure when refilling the circuit after everything is replaced that you bleed the radiator (there is a small plastic bleed screw at the right-hand end of the radiator that needs to bubble through with the engine running before securing this then topping up the expansion vessel to the line so that bubbles / airlocks are forced through before the system is sealed).Hi and welcome, you have already been given plenty of good info so should point you in the right direction. Your thermostat housing is prone to becoming brittle as I've just found out, if it is anything to do with that then it's a replacement, for a 1.4 petrol it cost me £91 from Audi.
Have faith you have bought a wonderful little car with a great following, nothing is impossible when you have the full support of A2OC's members.
Regards, Mark