The critical thing with the stat replacement is how confined the space is immediately behind the alternator where you need to get in to undo a couple of bolts securing the stat housing (plastic moulding) that have both a hex head and an allen socket in the middle of the head. The consensus here was that a hinged or angled 10mm ratchet spanner was useful, along with a low profile 1/4" socket adaptor that goes through the ratchet, with a 10mm socket on it (it needs to be long enough to reach but shallow enough to get into the gap if that makes sense) so just using the 10mm ratchet spanner alone wouldn't work. The other tool which was absolutely key I found was a set of ball headed long allen keys that I picked up in Lidl - these allow you to spin the bolt once the ratchet has released it.
Firstly uncover the engine - 3x 10mm nuts, remove the cover and put on one side.
To get down to the stat in the first place you then need to remove the boost pipe returning from the intercooler - this is a couple of jubilee pipe clamps - undo the one at the front to disconnect the joint, and then having loosened the one to the side of the engine, rotate the boost pipe upwards so you've got space below to get down to the thermostat housing.
A2 > Audi Workshop Service and Repair Manuals > Power unit | 3-cylinder TDI unit injector engine (1.4 ltr. 2-valve), mechanics | Engine cooling | Cooling system | Removing and installing thermostat
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is useful, although they specify a lot of tools and stuff that are "ideal situation only" - for instance, to release the coolant return pipe from the thermostat housing end. I couldn't get into that space with the release tool so left the pipe attached.
Once the housing bolts are removed, pull the housing off the thermostat. This will almost certainly break off a couple of plastic fingers that form an essential part of the workshop manual instruction list - if they haven't been broken off already in a previous stat replacement job. The thermostat normally stays in the block secured by the o-ring. Cover up the alternator with a plastic bag or similar, because unless you've drained the coolant circuit by now the coolant loss will occur next. Remove the old o-ring, and remove the thermostat. Use some of the spilt coolant to prewet the new o-ring.
Put in the new thermostat, followed by the new o-ring. Replace the housing (without the fingers you don't need to twist it onto the thermostat). Put the bolts in (this is fraught with risk of dropping the bolt into the bowels of the engine bay), turn anticlockwise before threading to minimise risk of cross-threading, then use the allen key to spin them in, then use the socket to tighten off. Replace all other removed parts, and remove any bits of plastic sheeting used to cover the alternator. Refill the coolant circuit with new coolant ; then run the engine to shift bubbles out including bleeding the radiator bleed point and then the expansion tank.
