A4 1.8t 2002 - rapid erractic readings on temp gauge for a while then no reading at all.
(if you just have low readings that alter slowly then it's more likely to be the thermostat)

Just thought I'd post this although I know it's been done before much more comprehensively with photos elsewhere on the forums - read them first and come back here if you're stuck.
Problem I had is that my car appears to have more hoses, wiring etc getting in the way that most of the other guides I've read on the net, so I'm posting this for anyone that runs into similar problems.
As we know the sensor is at the back of the engine and you can just see the wires coming off it if you look in from the side. Taking off what hoses, pipes etc you can that are in the way actually makes little or no difference, so don't bother! (I tried)
IMPORTANT - only work on a cool engine and unscrew and then rescrew the radiator cap first.
Shine a torch in and around from all angles first so that you get a really good idea of what you're up against. My first problem was that the handle of the little clip holding the sensor in was actually facing the engine and is impossible to get your fingers anywhere near and it wouldn't move around to the other side. I could see it through the wires and hoses from the top (it has little edges on it) so managed to pry it off with a long screwdriver - tried to avoid dropping it but it disappeared at the last second of course! (make sure you got at least one spare clip with the sensor you bought).
It does feel like there's no way you can get your hands in at the back but you do have to kind of force them past the hoses and try different angles until you get in there - it is possible, just doesn't feel like it at first!
You then wiggle the sensor and wiring holder around a bit until it comes loose with a pop - does feel like it's totally stuck fast at first.
Bend the little plastic bit at the top of the wiring holder up a bit to allow you to remove the sensor and then insert the new one - it should click back in but mine wouldn't actually click so I will have to keep checking it's still firmly on every once in a while.
The rubber ring may or may not have come off with the sensor, make sure you've removed it and put the new rubber ring in the hole making sure it's firmly seated. With the wiring attached to the new sensor put the whole thing back into the hole and try to ensure it's pushed in as far as it will go - it might seem to be a bit wobbly but try to look down and see or feel with your fingers if it's gone in far enough past the little slots at the side of the sensor holder pipe so that when you put the clip back in the inside edges of the clip will be on top of the sensor.
TRICKY BIT - getting the clip back on. Fortunately it goes on from the bulkhead side towards the engine. Firstly get your hands comfortably in there as far as you can, pushing past any obstructions firmly (without doing damage of course). It's a tricky angle as you need to be pushing it in level but your fingers can only manage it at an angle. I first felt for the little slot on the left and made sure the clip was in there first and then pushed it down at the other side until it looked like it was about right - really take your time with this part, be very patient and relaxed!
Push it in and then check and recheck as far as you can that it has located in the slots on each side - you can feel it with your finger tips rather than see it.
Moment of truth - switch on engine and allow it to fully warm up, keeping an eye on the sensor for any coolant leaks.
Such a pleasure to see the gauge reading half way again and just £8 for the sensor saved a fortune.

It was probably more like half an hour rather than the 5 mins others talk about but it's done!

Check for leaks on a daily basis at first, just in case the clip wasn't properly on.
Good Luck!