It is a thermostatic shut off type control. We have a Blackstone dryer with that type of control and Westinghouse introduced a model with that, the D6 introduced in 1953, I believe. It had a perforated drum and settings from 1 to 10 to select dryness. Later the auto dry control had just one setting--toasted. Of course, those machines also offered timed dry as well as auto dry.

This style dryer was also marketed by APEX and Speed Queen; the APEX was also available with a glass window in the door, like their dishwasher for a time.

Yes, Glenn and when the selected temperature is reached, the dryer shuts off, at least Westinghouse dryers shut down, boom.  I do not know if any of the other dryers had a cool down sequence or not, but the final temperature is much higher than the final temperature  reached in a regular auto dry system. Many of the time-temperature auto dry termination systems, up until the introduction of electronic dry controls, tended to overdry, but not like these systems.  John has a Blackstone with a similar dryness control. He can tell us what it does.

Glenn, as i understand it, there is a thermostat that functions like a high limit thermostat that terminates the drying.  Fortunately, with some of these it is adjustable for varying degrees of dryness. The Westinghouse dryers ran until the load reached a temperature of well over 200F, close to 250F, without the heating element cycling to make sure that everything was DRY like the dial or button was marked.