What is a single conductor temperature sensor called?
This task is often performed by a theromocouple, such as EMFields describe.
However ...

Your device is a "Capillary Thermostat". The sensor is filled with a substance which increases in pressure with heating and a bellows in the control end actuates a switch at a preset temperature. Once broken they are essentially not repairable.

You may be able to find a direct equivalent elsewhere and other versions which cover the same temperature range and which have the same electrical contacts could be used as a replacement.
As ever, YMMV.*

Another seller here - $ unknown.

Often a very good source if they have something suitable.



[Wikipedia - also known as a 'freeze stat'])(http://en.wikipedia.org/wiki/Freeze_stat)

Real world examples

and more

Lots of pictures - all linked tro related web pages.



*YMMV - Your Mileage WILL Vary.