Yes, the manual controls on the ceiling plenum include a thermostat to maintain the temp you set it at. On every a/c unit I've ever seen, the plenum controls consist of a on/off/fan speed control and a thermostat. Typically no temperature numbers on the thermostat, so you play with it until you find the position that maintains the temp you want, and then never touch it again.
Your current wall a/c thermostat may be electronic. Impossible to tell without a picture or opening it up to see if there's a circuit board inside. But, no matter really. It will not work with the Penguin a/c. If you want a wall thermostat for the penguin, you'll need to buy their CCC. And make sure the a/c unit is the correct model to work with the CCC.
The number 10 smells like bacon...