

If I had that setup, I’d use a power monitoring plug with a room temperature sensor. The combination of power monitoring and a temperature sensor would provide an amazing amount of flexibility.
For instance you can monitor when the compressor shuts off (because the current draw will drop significantly) and use the plug to shut off the entire unit, then power it on when the room temperature rises to a set point. I’d change that temperature setting depending on the time of day and possibly add a occupancy sensor or use light switches to enable and disable the AC when someone’s there. It would take some tweaking to get it working properly, but you should be able to make your room more comfortable and save energy with this kind of setup.
In my experience the thermostats of window units are crappy at regulating room temperature. Even so, did you miss this part of the post?:
The OP is planning on letting the unit run for 10 minutes and then turn it off, a much less effective solution than setting up a remote temperature sensor and power monitoring switch, and much better than having to control room temperature by adjusting knob that’s “labeled from 1 to 8 with 1 being warm and 8 being coldest.”