Where is the engine coolant temperature switch located

If you are are a skilled DIY repair person: test your fans by putting 12V to the fans directly. the connectors (easy to find, FAT wires). are under the driver side engine cover, behind the driver side head light.

If fans work, then it could be the coolant temperature SWITCH (NOT the coolant temperature SENSOR that feeds the ECU and the instrument cluster), typically located (not sure on 3.0 engine) in the lower radiator hose.

Visit the on-line store, know as reliable-store, they have the repair manuals. I'm sure you will get the solution of your problem.
Audi Service Repair Workshop Manuals

I have attached a picture to help you locate it

First time you might check the thermostat operating.

Heed of antifreeze coolant temperature!!!

The thermostat location for a 2000 Audi A4 1.9 TDI is on back of the alternator at the bottom side of the bracket.

IMPORTANT NOTE: It is NOT necessary to replace the alternator if you want to change the thermostat !!!

Thermostat checking:
1. Cold engine. Start up the engine and watch of the water temp indicator. After first value 60 Celsius Degree you still warm up the engine until the lifter (pointer) reach 80 C deg. (second mark after 60 C deg.). At this time you let engine running at idle speed and check with your hand the thermostat plastic housing and hose temperature in bottom left side of the engine. Heed of alternator driving belt and ventilator fan !!!
2. If the thermostat is good the hose must be cold until the water temp indicator reach almost 90 C deg.
3. The thermostat opening temperature is 87 C deg.
4. If the hose is already warm the thermostat is out of order.

Thermostat location, Part number: 044121113, in german - "Kuehlregle" (Price around $25):


Important note: Always replace the thermostat round seal, position 7 in the above picture.

Some cars have a sensor in the coolant overflow tank. If you look at the tank there should be a low and full mark. Make sure the fluid is between the 2.

SOUND LIKE FAULTY CLUTCH FAN OR THE AUXILIARY ELECTRIC COOLANT FAN NOT RUNNING. CHECK AUXILIARY FAN FUSE AND RELAY. IF LOOK GOOD HOT WIRE TO SEE IF FAN TURNS ON IF NOT FAN FAULTY. IF FAN RUNS YOU HAVE FAULTY THERMO SWITCH. WHICH LOCATED AT THE BOTTOM OF RADIATOR ON THE LEFT HAND SIDE OR ON THE LOWER RADIATOR HOSE ON THE RIGHT HAND SIDE OF THE ENGINE COMPARTMENT.IF FANS OKAY COOLANT LEVEL CORRECT.REPLACE THERMOSTAT.HAVE RADIATOR AND ENGINE FLUSHED.CHECK IN FRONT OF GRILLE MAKE SURE NO DEBRIS BLOCKING OFF AIR FLOW THROUGH RADIATOR CORES AND AC CONDENSOR CORES.

The Engine Coolant Temperature (ECT) sensor location on 2004 Audi A4 Diesel

ON ALL A4 MODELS AND I THINK THE A3 , THE ENGINE COOLANT TEMPERATURE SENSOR IS LOCATED AT THE REAR OF THE CYLINDER HEAD,WHILST ON SOME ENGINES, A SECOND SENSOR IS FITTED TO THE RADIATOR OUTLET PIPE...HOPE I WAS OF SOME HELP TO YOU....

you may have a worn out carbon brushes on the motor.

pull out the motor and replace the brushes...

tnx 4 using fixya,

drcool

I HAVE A AUDI A4 52 PLATE AND ON ALL MODELS THE ENGINE COOLANT TEMPERATURE SENSOR IS LOCATED AT THE REAR OF THE CYLINDER HEAD,WHILST ON SOME ENGINES, A SECOND SENSOR IS FITTED TO THE RADIATOR OUTLET PIPE...IF THE FAN MOTOR IS GOOD TRACE THE WIRES BACK TO SENSORS CHECKING FOR BROKEN WIRES.