Tempeture sensor on a tdi 1998 a 4

normally one
it is near the thermostat housing and has up to 4 wires attach to the plug
it is used to repot engine coolant temperature to the ECM so that air/fuel mixture can be adjusted and the fans switched on through a relay
don;t confuse it with a coolant temperature sender which has 1 wire and works the temp gauge

first check radiator level if it is full and the heater is working good make sure temp gauge is functioning c orrectly it is most likely the coolant temp sensor but if this is a high milage vehicle and you have owned long time and never changed i would also replace thermostat and check plug to temp sensor forr good conections and good wires

If the Check Engine light is coming on the computer is storing a code to let you know what the problem is. Have your computer scanned and you will probably find out what the problem is. The temperature gauge cannot work properly if the cooling system is leaking. The sending unit has to be in the coolant to work. If the coolant is low, the sending unit will not be in the coolant. If the coolant is leaking from around the radiator there has to be a radiator, radiator cap, or radiator hose leak.

In the temp sensor housing on the right side of the cylinderhead which has either a square 4 pin blue sensor or a semi rounded four pin sensor which can be black or green, the green ones are the latest version!

Sounds like you have a short to power or ground somewhere. Follow the wires from the sensor, and find it.

How many wires 1 ,3 or 4 and colours on lambda sensor? on most lambda sensors the Black wire is the sender wire but on yours I`m sure its blue ,as for the tacho gauge you need a wiring diagram for the ECU as you need to connect it there or pull the dash clocks out (carefully)

Replace cluster or send it to model electronics to check it out and repair,

Yes it is that easy. It should be a 4 pin connector located on the transmission side of the engine head in a plastic flange. Best is to wait for the engine to be cold. Unscew the radiator cap to relieve pressure but screw it right back on. On the 2.0L engines when you unclip the coolant sensor little or not coolant loss will happen if you do this. Just unplug it, pull out the clip, pull out the sensor, and the seal which sometimes stays stuck. Install the new sensor with a new seal lubricated with some coolant, make sure it's well seated and reinstall the clip. The sensor is well seated if the clip fits right over the top, just make sure both sides clipped into position. Replug it fill the coolant with VW original coolant mixed 50-50 with water if needed and done. If you have a fault you might need a scanner to erase the check engine or fault in the cluster.

What's the reason for changing it? Eratic temperature readings?

this is one of three posabilitys or it could be the guage or the wirring to the guage

P2181 Cooling system performance

Check Thermostat operation & Temp sensor for ECU. CHECK ENGINE CCOLANT TEMP SENSOR IN WATERHOSE, NORMALY A 4 PIN PLUG. ON SENSOR SELF PIN 1&3 OR C&D AT 0 degrees
5000-6500 ohms,60 degrees 530-675 ohms,90 degrees
200-275 degrees

Could also be the cooling fans - I've heard of fixing it by replacing the fan motor and clearing the code as well. The easy fix seems to be the coolant sensor though - I've seen several online threads where owners cleared this code by changing that sensor.