Yes, and I really don't think it matters which wire goes to which (+/-) as long as both are connected and it can measure resistance. There's no question it will work if you get a separate temp sensor. I just sold this one with the temp sensor, and as you can see in the pics, I hooked it up and made it work even out of the car.
Jeep Wrangler Cherokee YJ TJ LJ JK XJ KJ Auto Dim Compass Temp Rear View Mirror | eBay
What I was suggesting is to see if hooking up the mirror directly to the climate control temp sensor that's already there might work. It may work fine, it may be that having the signal go out to 2 different sources/sets of wires (climate control and mirror) messes up the signal, and it just can't be done. Can't hurt to try it for free, though.
