What you are looking at is the capillary tube which is part of the thermostat and the far end of it has a small bulb which sits against the cooling plate & transfers the temperature reading up to the control switch. You have to locate the far end of tube & remove it then pull the tube out with the thermostat. The new one will have the capillary tube rolled up & you have to straighten it out carefully so as not to break it.
Lincoln Appliance NZ, January 2010