My first floor thermostat is an Ecobee and is poorly located in my dining room directly below the register. This is a BAD location for a thermostat. The cold air will blow over the thermostat, causing it to read colder than what the rest of the zone is. The other rooms will be warmer than what you want and your air conditioner will constantly go on and off, which will significantly reduce the life of the air conditioner. It is time to relocate it.
Check out my review of the Ecobee thermostat
SOLUTION
The easy solution is to relocate the thermostat on the opposite side of the wall. Remove the thermostat and take a photo of the existing wiring for future reference. I pulled the wiring out as much as possible and taped it to the wall so it wouldn’t fall behind the wall.
Always take a picture of the wiring before removing. 
I pulled the wires out. 
I taped the wires while I work.
I drilled a hole on the other side of the thermostat to locate the new position on the other side of the wall.
Then I cut a new hole on the opposite side of the wall to run the wiring through. Then, I installed the thermostat mount and pulled the wire through. I used needle nose pliers and slowly and gently pulled the wires through. As you can see below, I also covered each wire tip with scotch tape so they don’t touch each other and spark. These wires are low voltage so you will not get electrocuted touching them.
I drilled 3 hols on the other side to give me room to pull the wires. 
Carefully pull the wires with needle nose pliers, do not damage the wires. 
I mounted the thermostat bracket
I then pulled up my photos of the previous wiring and copied it. Afterwards, I put back the Ecobee thermostat and made sure it still worked.
PATCHING THE HOLE
The next step is to patch the hole left by the thermostat. I took scrap wood and screwed it on the inside of the wall at the top and bottom of the hole, so the new piece of drywall can be screwed in. Since I am renovating my house I had scrap drywall, but if not check Craigslist. People are always throwing out some scraps of drywall. If that fails, Home Depot sells 2’x2′ pieces of drywall for this reason. Don’t forget to match the thickness of the new drywall with the thickness of the old drywall.
Next, its time to tape the edges. I am comfortable using standard tape, but if you are not use the self sticking mesh tape. If either of these options scare you, home depot sells these patches that are supposed to be very easy to use. Finally, paint it.
STATS
Time: 15 minutes to move thermostat, 30 minutes to patch and paint (does not include drying time).
Cost: Patch $4, joint compound 3lbs $6, tape $2.18
