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Evensville is located in Rhea County, Tennessee. There are roughly 3,654 residents, living in 1,397 households. The average temperature for Evensville this time of the year is low of 61F and high of 84F. On average, Evensville gets about 4.36 inches of precipitation in June. Most residents are home owners (80%), have a high school diploma (66%) and are married, no kids (37%).