Petrol?
Coolant level okay?
If the engine coolant temp sensor has failed the ecu will put the fan on full speed as a precaution, you can plug a new one in to confirm before doing the actual change. The sensor on the revised version of the thermostat (pic below) is easily changed, with a little coolant loss, by creating access, pull the horse shoe clip, pull the sensor out, push new in and re inserted the clip. Make sure the engine is cold, and you have the new sensor close to hand.
Depending on the age of the car you might have an early/original version of the thermostat housing which had the temp sensor and electronic thermostat in one, which in a service bulletin would have had a temp sensor fitted into the bleed screw hole otherwise the sensor is beside the bleed hole screw.
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