Who built the very first wood burning stove?

Benjamin Franklin is generally credited with the invention of the wood stove.

The development of the wood stove is rather more complex than a single invention, however. What Franklin did was to improve on the fireplace with an iron fireplace insert that heated air from the room and pushed it back into the room to warm it. Some people would say this was not a wood stove, so much as an improved fireplace, leaving the actual stove to be invented by someone else. Others might object that other inventions anticipated Franklin's, so the invention should be ascribed to someone earlier. Nevertheless, if you want a name of an individual, the best name to choose might be Benjamin Franklin.