Gary Does the car have a temp gauge or warning lamp? If it has a warning lamp there is a back up sensor for overheating on o/s of cylinder head(blue 2 pin block with only 1 pin).(fitted to some vehicles) The engine ecu thinks its overheating so grounds the fan relay constantly as a precaution.
Presume you have changed the green engine man sensor and coolant live data is ok?
Any open circuit wiring on these circuits will also cause this to happen.