Hi Lars,
I have been through this thermostat fault in the last year. I had the same code 41729 but not the 02851 code. My experience is
here but I must get round to to completing the thread, I hate threads that just end in mid air with no conclusion.
First I have to say why are you focussing on the temperature sensor when the reported fault is the thermostat? The temperature sensor produces its own fault code, I know!
In answer to your question the temperature sensor and thermostat are both attached to thermostat housing situated at the upper right (facing the car from the front) of the engine block, well hidden under the upper inlet manifold and other things in the way.
A new Mahle thermostat housing and attachments.
Replacing either is a bit of a pig of a job which is why I let my mechanic do it!
I see you have the link to Sarge's excellent fresh post, but here are alternatives
A2 > Audi Workshop Service and Repair Manuals > Power unit | 4-cylinder direct injection engine (1.6 ltr. 4-valve), mechanics | Engine cooling | Cooling system | Removing and installing coolant temperature senderG62
workshop-manuals.com
A2 > Audi Workshop Service and Repair Manuals > Power unit | 4-cylinder direct injection engine (1.6 ltr. 4-valve), mechanics | Engine cooling | Cooling system | Removing and installing map-controlled engine cooling thermostatF265
workshop-manuals.com
I am convinced the Audi's OEM suppliers for the thermostat housing, temperature sensor and thermostat were Mahle, notice the scratched out Audi rings in the pictures!
A word of caution, the thermostat housing is likely to be very brittle take great care. My advice is to buy the housing and fittings as one item, probably not much difference in cost to buying the thermostat and sensor separately. This way if things go wrong you have the housing to hand but this is a much bigger job, said to be worth doing from a preventative maintenance viewpoint for it is known to leak with age.
I bought this, the cheapest I could find at the time...
Find many great new & used options and get the best deals for Thermostat Coolant TM5109 by HELLA - Single at the best online prices at eBay! Free delivery for many products!
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Hope this helps but it has just struck me you will be LHD which might make replacement even more difficult!
Andy