Before you spend money on a sensor replacement, it would be well worth while to check that the sensor really is the problem.
The Jazz doesn't have a dash temperature gauge to show the temperature, but, the engine temperature can easily be read by plugging in a cheap, readily available OBD2 reader (£10 ish) into the diagnostic port which will be able to show you the temperature that the ECU is actually reading from the sensor.
After a night not running, it should show pretty much ambient temperature, then start the car, watch it rise and just see what happens.
If it looks OK but the fan isn't running, then suspect the fan temperature switch, and if the fan is running, look for other reasons such as a lack of coolant etc. Also, if the car has air conditioning, turning that on will cause both fans to operate to check that the fans are OK.
There are good vehicle technicians and there are also plenty of not so good ones ........