Correction, it's the Ambient Temp sensor, not the AC temperature sensor. It should be right behind the radiator as shown below.

Disclaimer: I'm not familiar with Vitz at all. This is something i just pulled off the internet..
Ask mechanic to pull it out for you and you can test it yourself.. There should be two pins on the sensor. connect multimeter on resistance settings to both of these pins.
1. It should not be open circuit. If so, replace it,
2. Note the resistance and at various temperatures.. Resistance should be higher at higher Temperatures... Put it in refrigerator and note again. if you find inconsistency anywhere, replace it.
your climate control function won't properly in absence of this sensor but you should be control the AC manually.
On a second thought, are you getting the same engine stop issue after clockspring replacement.?? The clockspring do not directly house a CANBus wire but the SRS module is definitely connected on CANBus.. Maybe the source of problem was Clockspring and not the Temperature sensor.