Falcon au 2000 thermo fan not running when hot

Bad coolant thermostat. Faulty thermo fan sender switch. Thermo fan motor burnt out. Bad thermo fan relay. Radiator core blocked. Low coolant level. Temperature gauge and/or gauge sender faulty. Ground leads have a bad connection (corroded/broken/fouled from oil and grease/bolts or screws loose)

Why did you replace the fan relays? Obviously nowt wrong with them. You should get car diagnostic tested to verify fault.
It will save you loads rather than guessing.

Have you even tested for live feeds and earth faults?
Have you checked the fuses? Did you short out the relay to see if the fans actually work?

a bad thermo probably wont cause the fan problem. It may be a coincidence but fix the problem. No fan? sensor, relay, switch, fuse, short? Start w the basics. are both rad hoses hot when running, if not- (thermo problem?)

in a plug on the side of the gearbox under the car (16mm),running in "D" with the engine running at 1000 rpm with the box warm but not hot,pump it in until it runs out of the plug, a pit,hoist or solid ramps will be needed for this as well as 2 people

Some fans do keep running after engine is switched off for a short period of time (up to 5 minutes) Check with a service person (ford) to see if that is the case or if you have a faulty sensor.

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REPLACE THERMOSTAT AND RADIATOR PRESSURE CAP.CHECK MECHANICAL COOLING FAN.SHOULD HAVE RESISTANCE WHEN TURN WITH HAND.IF FREEWHEELS FAN CLUTCH NEED TO BE REPLACED.CHECK TO MAKE SURE AUXILIARY ELECTRIC COOLING FAN RUNNING HOT WIRE COOLING FAN IF FAN RUNS.YOU HAVE FAULTY THERMO SWITCH LOCATED AT THE BOTTOM OF RADIATOR ON THE LEFT HAND SIDE ON 4 CYLINDER ENGINE FOR V6 ENGINE THERMO SWITCH LOCATED ON THE LOWER RADIATOR HOSE ON THE RIGHT HAND SIDE OF THE ENGINE COMPARTMENT. CHECK FOR BLOWN COOLANT FAN FUSE OR FAULTY RELAY.IF THE AUXILIARY ELECTRIC FAN DONT RUN WHEN HOT WIRED THE ELECTRIC FAN FAULTY.

OVER HEATING AT A STANDSTILL PROBABLY COOLANT FAN NOT COMING ON.CHECK COOLANT FAN FUSE/RELAY.IF BOTH GOOD COOLANT TEMPERATURE SENSOR FAULTY.HOT WIRE COOLANT FAN.NO RUN REPLACE COOLANT FAN MOTOR.IF FAN MOTOR RUN.FAULT IN FAN MOTOR WIRE CONNECTOR.IF ALL IS GOOD YOU COULD HAVE A LEAKING HEAD GASKET.CHECK ENGINE OIL LOOK LIKE MILK SHAKE HEAD GASKET BLOWN.

Radiator fan is supposed to start working after the temp reaches a certain limit. And it is supposed to run til the temp reaches a certain lower limit. So when you switch off the engine and walk off the fans must be running to cool the water to that lower limit. Unless you seen that it runs well past that and does not stop at all. Does it start running when you start the engine? And runs throughout the time the car is running, which it should not. The relay seems to be out. It is this relay that controls the running of the fan. or the temp gauge. If the temp gauge is giving wrong temp then the relay has to keep working. Please check both, the relay and before that the temp gauge.

Check that the fans are still working .Check that the thermo switch is working.Check that you have power to the thermo switch. and if not check relay/supply of power.Unsure with your model but the thermo switches are usualy screwed into the radiator but could be mounted on the engine.You can check your fans by running a piece of wire from the positive terminal of the battery to the positive side/wire of the fans.As long as the fans are earthed as well they should work and if not then the fans will need to be replaced.