UK Auto Repair Questions?
The first stage of diagnosis should be a full diagnostic code read to establish what codes if any are present. From there a diagnostic path can be established.
I suspect however that there won't be a fault code because the Temp Sender is working however it is giving a wrong temperature that the Engine Control Module is acting on rather than the correct temperature. What you need to do is take a look at the Live Data readings for the Temp Sensor to determine if it is giving you the correct reading. If it isn't then I suspect you will want a new one.