Hi Steve I am also in NZ (Auck) This model does not have a thermostat like the old models so you will not get a click on/off. This model controls the temp. by having a sensor in each compartment attached to a control module in the back. The temperature control knob is a variable resistor. The fault you describe could be a faulty sensor, faulty variable resistor or a faulty control module. If there is a fault it will let you know by beeping. Count the number of beeps between each pause & that is the error code i.e. 3 beeps pause 3 beeps pause would be error code 3. If you are getting an error code let me know & I will look it up for you. Otherwise it would be best to get someone out to check those 3 parts. Not easy to do yourself.
Lincoln Appliance NZ, March 2013