Some things to consider
1. Faulty thermostat. Possible, but unlikely if fluctuations are rapid.
2. Faulty sensor. Certainly possible cause, but not easy to access.
3. Wiring fault. e.g. corrosion on wiring connectors,or damage to wiring harness.
Due to difficult access to the sensor, it may be a good idea to reseat the connectors at the rear of the instrument panel before starting to partially drain the cooling system, and remove various pipes from the engine.
Likewise connector D004A is located under the engine bay fusebox, and if water has got in there....
Two access the sensor, it is necessary to remove the air filter, plus housing and several air inlet hoses. I have been advised by Forum member,
@IceVovo, as a general rule, "remove anthing in the way".
Please note that there are two coolant sensors on the 2.8 JTD. One sensor is used by the ECU, for engine and cooling fan control. The second sensor is used for the temperature gauge, and I believe the overtemp warning. All the gauges on the X244 are operated by electronically controlled stepping motors.
If access is made to the sensor it may be possible to check it, by monitoring its resistance with a mutimeter while the engine warms up.
If the sensor needs to be replaced, the cooling system will have to be partially drained via the upper radiator hose. Access to the hose
is easier if the LH headlamp is removed. (Hold the adjustment nuts with a spanner when removing the fixing bolts.)
The air hoses need clic pliers to loosen the clips, while I had to saw off the cooling hose clips on the radiator. Identify the size, and stock up with worm drive (jubilee) clips.
Link to eLearn via 4cardata (Wiring diagrams) On linked diagram E4010 there is no earth connection on sensor K035. I believe that this is an omission on the original diagram.
Link to eLearn via 4cardata (Sensor location)
Please note that on the 4cardata version of eLearn, some of the desciptive text is cropped, just when it gets intersting, also some of the diagrams are unreadable.
For convenince I have attached my copy of the appropriate part of the instrument panel diagram, and my colour code translator. However on my diagram connector wiring detail is not incuded.