I have seen in the past the thermostat fitted the wrong way round....
Of course then the symptom would be overheating as the wax (?) vial would never get hot enough to open. As it happens, most housings are nowhere near tall enough to accommodate a reversed thermostat. Fret not though, there are other ways to royally c**k it up. Go on, ask me ...
Well, since you ask ... and I will tack the following onto one of the many thermostat / temp gauge threads ....
1) Original symptom was car taking forever to warm up, BUT my interior fan wasn't working so no hard evidence of this, just a non-moving gauge. Also, the tailgate micro-switch was duff, so Mini Dis position on dash was taken by false 'boot open' warning, so no MPG at that stage as possible warning of trouble.
2) Mistake one: assume because my other A2's had needed thermostats, this one did as well, therefore failed to test the thermostat in the most basic way: feel the hoses.
3) Mistake two, despite having full fat VCDS and knowing I should do it, failed to plug it in and compare gauge and ECU readings.
4) Mistake four, buy pattern (Borg and Beck) thermostat.
5) Mistake five, fit said thermostat with supplied O-ring rather than original style seal that is more of a tyre located around rim of thermostat..
6) Test drive car: gauge still failed to register.
7) Mistake six, still failed to carry out test as per mistake two.
8) Mistake seven, swap out temp sender without doing basic resistance tests.
9) Good moves (finally) 1) Buy genuine thermostat, 2) spot old seal in workshop bin and reinstate as new stat doesn't come with one, 3) With new stat installed rig VCDS, lift idle speed with heater on full, fan off, watch VCDS instruments vs engine vs temp gauge. 4) Keep feeling hoses, now absolutely stone cold unlike before.
So the good news: whilst there is a very slight difference between engine and cluster temp sender readings, the gauge is reading absolutely identically to the engine temp side of the sender. Therefore I'm calling the Febi sender good. The old sender was tested and at ambient temps showed 1500 ohms on one side and 2500 on the other: it was duff.
Conclusion: the original thermostat was likely fine. Had I merely driven up the road for a mile and put my hand on the rad hoses I'd have known for sure.If the stat was good, the hoses would stay cold for at least a mile or so. When I fitted the pattern, in retrospect the coolant was probably leaking around the outside of it, quite aside from when it actually opened.
Therefore, the problem was almost certainly the sender. By time I had activated Mini Dis I had already messed up the thermostat, hence the dismal economy. I.e. I had literally swapped two issues over: gone from a failed sender and likely good thermostat to good sender and misinstalled thermostat.
So lessons for the future:
a) Seals aside, the pattern stat doesn't fit very well, use genuine that locks into place properly.
b) If your gauge suggests the car is failing to warm up, feel the hoses after five minutes of running: on a TDi they should still be cold. If warm, irrespective of the sender, the thermostat is either stuck open or opening too early.
3) The sender is easy to test via VCDS by comparing measuring blocks, temp, in Instruments VS same in Engine. Easier still, with unit out, start by comparing readings on the two pins next to the curve vs two pins next to the flat: if wildly different, sender is duff, if close you'll need to find actually resistance readings at particular temperatures.
Phew! Onwards I feel ...
EDIT: I forgot to say, the genuine thermostat never did open on my test and that was with VCDS and gauge saying 94.5 degrees at one point. The thermostat is labelled 89dC, but the sender is in the head, the stat is down at the base of the engine where it'll surely be cooler. Therefore I think it's safe to conclude that if your rad hoses (particularly down near the thermostat housing) have any temperature in them before the gauge shows, say, 70, you have a thermostat issue.