Well, here's a guess and a question:
Since you say that "There are a number of wires behind it in the closet", perhaps the use is to warn if the actual temperature goes outside of the upper or lower settings.
Can you take it out and have a closer look, and perhaps show us the wires, and the back? Maybe you can find a manufacturer's name and/or a reference number, something to Google for more info.
It's an interesting mystery, until someone can tell us what it really is...
“Courage is being scared to death, but saddling up anyway.”