What is the function of the thermal cut out switch on a AEG cooker

My AEG cooker switches itself off after about 15 minutes, the light in the oven goes off and even if you increase the set temperature on the thermostat the "heating" light does not come on. After about another 10 minutes it seems to reset itself and functions again but then the cycle repeats. The oven is fitted with a cooling fan that keeps the controls at a reasonable temperature. If this is not functioning a thermal cut out operates and closes everything down, which is what is happening. I took the top of the oven and confirmed that the cooling fan was not being powered up because the inline thermal cut out had failed. Looking at other blogs it appears that the purpose of the cutout is simply, to provide an overrun so as to carry on cooling the oven when it is turned off , it is not to protect the fan! Is this correct?

Sounds like the case thermostat. It cuts the power if the case overheats, to protect against setting light to other nearby items.

Check the case fan, which should keep the external case cooler than the oven. Check for blocked airflow, dust, oven insulation which has come loose, etc, and anything else which might make the case overheat.

Another common cause is the connections to the case thermostat itself, which can go bad over time causing localised heating. If they are push-on connectors, pull off and push on again to clear away any oxide which has formed. If the connections aren't tight, pull off, close the connectors slightly with pliers, and push on (it's easy to over-do this, so don't close up the connector sides too much).

The same might have happened with the stat's internal contacts, but they are not usually repairable, and it would need to be replaced if that's the case.