As defined by the Encyclopedia of Alternative Energy and Sustainable Living, a grain-burning stove is "similar to an ordinary wood stove in appearance (but) is designed to burn grain. Grain is a good, renewable fuel ...Typically, a grain-burning stove can use all grades of hulled wheat, rye, triticale, peas, faba beans, and corn, as well as other biomass fuels, such as cherry pits and wood pellets. It's recommended that the grain be cleaned before use. Oil seeds and grains with high hull content such as barley and oats don't work well in the stoves."
"Corn is a fuel that burns clean and does not require a conventional chimney," explains Justin Thomas at TreeHugger.com. "You can vent corn stoves outdoors by using a type 'L' or 'B' double wall vent."
For the more technical aspects, we'll call on the folks at GrainStoves.net: "Grain needs to be heated to 1100° before it will burn. However, in order to get the grain to the requisite temperature, the entire stove needs to be heated and all the moisture must be driven out of the grain. As the moisture content of the grain increases, so does the amount of energy required to drive out moisture. The more heat being used to drive the moisture out, the less heat is available to maintain the 1100º burn pot and heat the house."
Whatever grain you choose, you'll likely burn up to one bushel per day in the heating season.