Can I put a thermostat on my wood burning furnace?
Yes: read the manuals here: http://www.woodboilers.com/discontinued-boilers.html  and you'll see some of the issues.

The key difficulties are:


Regulation of a wood-fired furnace is a very non-linear process, and depends a lot on what fuel is already in the furnace and how it is burning.
You don't say what happens when the limit switch gets hit.  Some units need to be manually reset, some don't.
You can burn out the blower if you try to run it when there's no fire in there
If you throttle the blower due to input from the thermostat, you'll get a huge amount of creosote buildup in your chimney.


Most of these conditions fall out if you keep the fire fed regularly and you have a wide boundary between high and low setpoints, and you only run the furnace when it is cold outside.

However, it works far better to burn the wood fairly consistently and use that to heat a gigantic tank of water and to use a thermostat to move that hot water around the house.