bigpapa, just a guess, but I'm thinking stefuel has a self-contained air conditioner that comes with a remote control that allows you to turn it on and off. And when it loses power it doesn't come back on, regardless of where the temp control was set. And I'm guessing that the digital thermostat is just an extra thermostat that he has available if it would help to fix the problem, but is not currently part of the system. Am I right stefuel?
Now granted, I suppose he could install the thermostat in the room, and if it reads a temperature that the room would never reach when the AC unit is working, it could send a toggle power to the unit. Then wait several minutes and see if the temp goes down. I don't think that's a very good solution but it could probably be made to work.