Theory of disc thermostats

Perhaps this should be in the appliance section but it is to help my understanding rather than a practical question.
My oven case cooling fan circuit disc thermostat has three wires connected. One is permanent live from mains input via the fan, one is to mains return and one is switched to live by the oven selector switch.
How does the internals of the stat operate with this arrangement?
I can work out how it would handle a simple switching operation across live and return but not with two seperate live supplies.
(It operates a tangential cooling fan motor, and I wondered if there was a need for a starting current? )
Thanks for any teaching offered.

It may have a Neutral to supply a bery small heater inside the thermostat. This heater is connected between Neutral and Switched Live and reduces the difference between the ON and OFF temperatures for the thermostat.

To expand on Bernard's reply ...
Ideally you need the stat to have a very distinct "click" on/off - so the terminals snap open/shut cleanly. If they merely moved with the expension/contraction of the metal then there would be a lot of arcing and burning in the contacts. However, that means introducing quite a bit of hysteresis - ie things warm up, the stat goes "click", then things must cool down considerably before it clicks again and turns back on. In some stats the hysteresis comes from (eg) a metal spring flipping between two states, in others there is a magnet that holds the contacts together when closed but has a lower pull when the contacts are apart.
So the small heater is added so that when the stat turns on, the heater artificially warms up the stat. If it's done right, the additional temperature added will cancel out the mechanical hysteresis and give a stat with a very small on/off differential.

As a previous job, we had some AC installed that used chilled water for cooling and hot water for heating - two water coils in each fan-coil unit, controlled by two valves wired to a stat on the wall. These two setpoint stats had no anti-hysteresis heaters in them - and the response was terrible, especially combined with the slow response times of the wax-capsule valve actuators.
One was so bad that the room had to heat up by something like 3˚C before the stat would turn off again. This alone was uncomfortable because it made the room go hot and cold in cycles. But it was worse - with the lag in the valve closing, the room would actually heat up enough to then turn on the cooling So the system would cycle between heating and cooling
At some point, we replaced the wall stats with electronic controllers (which also automatically changed fan speeds). In part, to remove the opportunity for users to "fiddle" with the settings. At the risk of sounding sexist, I observed that it seems to be a female thing to turn the heating off* because it's too hot - and then complain the next morning that the office is cold without having had the heating on
* It seemed that few could understand the idea of turning the thermostat "down a little" - all controls got operated as a switch with the only setting used being "full on" and "off", or in teh case of air conditioning, "full heat", "off", "full cold"

Thanks to both---my oven is working (based on the acquisition of a replacement stat) and my mind is settled (based on the acquisition of knowledge).