This is a design that I made recently. One option would be to adapt something like this into a circular frame for a mirror.
This is a sketch of a circular mirror in this theme. I superimposed the sketch onto the photo you sent me so you could see scale. (I realize it's difficult to see the sketch, but hopefully this gives an idea). It is important to note that the mirror at this size would be less than a foot in diameter (probably 11 inches), so it would not leave lots of functional mirror surface area. I would make sure that the section of the frame near the thermostat was made of shorter pieces of wood. In this design the thermostat is not obscured by anything.
This option keeps a similar design for the circular mirror, and it also has two wall-mounted candle holders. The candle holders would look very much like the first photo in this series. They would have a small platform coming out the front for a candle or light (perhaps with a mason jar, wine bottle, or other cylindrical candle cover). I am thinking I would mount the right one directly over the thermostat and put it on a hinge so you could swing it out of the way to access the thermostat.
This is a closeup on some lovely reclaimed barnwood that I have. I could use this piece (or wood like it) to make a more simple, minimalist, rectangular frame.
This piece is about 9.5 inches wide, so I would cut it longways down the middle so that the frame width would be about 4.75 inches all around.
I think the remaining blue paint adds a lot of character, but if you don't like it I could sand the paint off or use another unpainted piece. I do think it would look especially good with a subtle glossy finish.
This is about what the proportions would look like if you want to go with a simple barn-wood mirror. In this version the thermostat would not be obscured. The frame would be approximately 22 in x 36 in and that would leave approximately 14 in x 27 in of visible mirror (these dimensions are very rough--I would need to get more specific measurements; I am currently basing everything off of my attempts to keep things symmetrically spaced yet not obscuring the thermostat).
This is a rough drawing of the type of mounted candle holder I could build around the thermostat so that it would be accessible but visually obscured by a candle/light in a mason jar (or other cylindrical casing) when viewed from the front.
This would work with any rectangular or square mirror. Candle holders will, of course, leave less space for the mirror, so it would have to be less wide.
The platforms would hold cylindrical glass cases. I can make these out of mason jars, wine bottles, or pretty much any other fire-safe material that we can think of.
This is to give you an idea of the dimensions/layout of a rectangular barn wood version with wall-mounted candle holders.
The mirror in the center could be taller potentially. And we could tweak the design as needed (slightly rounded or angled corners, a thinner frame, etc).
In this version the frame is still made of 4.75 in wide barn wood, leaving the useable mirror width at only about 10 inches (according to my rough calculations based on this picture and the measurements you sent).