Delbourt

https://www.dtafast.co.uk/download_files/Manuals/S%20Series%20Manual.pdf
And page 146 and the next few.
Have you always had problems starting from cold? If so it may not be the cooling water sensor but if the problem is new it could be a.failing sensor, the wrong sensor, or resistance in the wiring that is affecting the ECU .
As far as I’m aware the sensor will change its resistance as temperature changes under normal circumstances.
It would seem logical to think that a small variation in resistance somewhere will give the ECU false information and inhibit the start up process.