Dunham was born in Coventry, Connecticut, on June 10, 1833. He was the son of Austin and Martha (Root) Dunham. The family moved to Hartford, Connecticut in 1835. Dunham's father was a merchant and businessman in Hartford. His father was in the cotton manufacturing business as well as the banking and insurance business – which enterprises Dunham took over later after his father's death. Dunham's maternal grandfather was Judge Jesse Root.
Dunham attended primary school in Hartford, and North Coventry. He went to high school in Ellington, Connecticut and graduated from there. In 1850 he entered Yale University at the age of seventeen. He graduated in 1854. His first job after that was as a teacher in Elmira, New York, for a year. He returned to Hartford after this.
Dunham was one of the founders of the Willimantic Linen Company. He was also a founder of the Austin Organ Company and the Automatic Refrigerating Company. Dunham was a director of the Etna Fire Insurance Company, the Travelers Life Insurance Company, and the National Exchange Bank. Dunham was a member of the firms of Austin Dunham & Company and E N Kellogg & Company and a senior partner in the firm of Austin Dunham's Sons, manufacturers of worsted yarns and hosiery. Dunham was later president of the Dunham Hosiery Company and the Rock Manufacturing Company and was involved with many other businesses.
Dunham bought the Hartford Electric Light Company as a bankrupt concern and developed a large business from it. He was president of the Hartford Electric Light Company (HELCO) in Hartford, Connecticut for over thirty years. Dunham was a pioneer in electrical application developments because of his company. Under his direction HELCO was the first public utility in the United States to transmit a three-phase electric current for a distance of several miles. He was the first to successfully connect commercial electric alternators in parallel, the first to use a storage battery in connection with a hydroelectric power plant to regulate power and the first to use aluminum commercially in a transmission conductor.
The Hartford Electric Light Company under the direction of Dunham was the first to adopt modern methods of transmission of energy from water power, the first to use enclosed arc lamps, the 60-cycle rotary converters, and the constant-current alternating arc-light system. He led the way to the adoption of the steam turbo-generator as a part of regular central-station equipment. Dunham also launched the Nernst lamp into commercial use.
Dunham became interested in the development of truck farming in his retirement. He bought a farm in Newington, Connecticut, and established some five-acre tracts. There he built concrete houses and barns. Additionally he improved the land to high productive farming. When the United States entered into World War I he gave the farm to the Storrs Agricultural School.
Dunham became interested in many charities in his retirement. His main one was the Hartford Hospital. Another was the Sheffield Scientific School and their Electrical Engineering Laboratory. In his retirement he was a trustee of the Watkinson Juvenile Asylum and Farm School, the Watkinson Library and the Hartford Grammar School, a director of the Cedar Hill Cemetery, and president of the Hartford Hospital Corporation.
Dunham made several trips to Florida and Cuba during in his retirement.
"Reminiscences of Austin C Dunham" – a series of autobiographical papers first printed in the Hartford Courant newspaper 1912–1913.
He was married September 16, 1858, to Lucy J Root, daughter of James Root who fought in the War of 1812, and Lucy Ann (Olmstead) Root. Lucy died in September 1864 when she was 23. Lucy Root was Dunham's cousin, since she was the granddaughter of Jesse Root's oldest son, Ephraim. They had two children. A son named George, who died in 1873 in his thirteenth year, and a daughter, Laura Baldwin. His daughter studied in the Yale School of the Fine Arts during 1876–77. She married Danford Newton Barney March 22, 1890.
Dunham died at St. Petersburg, Florida, on March 17, 1918.