 Greene County is named in honor of General Nathanael Greene, a hero of the American Revolutionary War.According to the US Census Bureau, the county has a total area of , of which is land and (0.6%) is water.In recent years, average temperatures in the county seat of Carrollton have ranged from a low of in January to a high of in July, although a record low of was recorded in January 1912 and a record high of was recorded in July 1934.