Let's just break it down backing up the useful information from Paul and others.
Thermostat. Assuming your temp gauge is reading normally, a knackered thermostat will open early (or is open all the time) and dumps all of the precious heat that the wee diesel generates into the radiator early - this is particularly bad on cold days or if you've got high air speeds straight away. The engine will struggle up to 70 degrees or so and then just stay there unless you're driving hard and suddenly stop (ie, traffic jam on motorway) - whereupon you will get 90 degrees for a few seconds until you have airflow again and then the temperature will drop off like a stone.
Temp sensor. As Paul has stated above, this is a double unit (green with 4 pins), both reading the same thing but sending info to two different places. Both sides are prone to occasional failure, but not necessarily simultaneously. Dash readout is useful, but is purely information. ECU readout governs which map set your ECU is using based on engine temperature - basically analogous to the manual choke you would decide to use 30 years ago while it was cold until it warmed up. If the dash side fails - you don't know what your engine is doing. If the ECU side fails, the ECU doesn't know what the engine is doing, so usually assumes that it is cold and chooses the lower performance higher fuelling maps to warm the engine up. This has the same effect as a knackered thermostat, but for a different reason - it will burn through fuel quickly and may also affect how clean your engine is.
My Tdi car had both problems when I bought it - thermostat and sporadic issue with dashboard temp readout although the engine side was probably normal. Replacing thermostat made it run better. Replacing coolant temp sensor meant I knew what temperature it was without using the ODBII reader. Both sensor and thermostat are easy jobs if you have the right small hand-tools and a bit of nous as well as following the various threads here instructing you how to do it.
One further thing. We get dramatic differences depending on the tyres. My other half has notoriously heavy feet which in her slightly badly-running 1.4i with a small tank means she gets 180-190 miles on a tank of unleaded before the light comes on and I get sent back to the refinery to get more. This is typical without fail for the last 7 months with no difference attributable to air temperature (I've checked both temp outputs suggesting thermostat and sensor are fine) - the fuel use has been more or less uniform under any conditions. We swapped over from the excellent Nexen winters to a new set of Aoteli summers 2 weeks ago at the same time as refilling the tank, and her car just went 204 miles on 27 litres, so would easily have gone 250 before the light came on. When I drive her car I get around 20% more economy than her, so I may be able to get it to 280-300 on a tank with a bit of effort, but then I'd have to prise the keys of the Island green car out of her hands which wouldn't go down well. Injectors next on the list of things to try to clean up the fuelling precision - but I was astonished by the improved fuel figures just from a set of wheels.
