There is no known biography of Thomas (T. A.) Carrington. All that is known about him is that he filed a patent for a type of range oven on July 25, 1876 in Baltimore, Maryland.
Some websites cite Thomas Carrington as the inventor of the range oven, but kitchen stoves with a similar design to the one in his patent existed as far back as 85 years prior and were common in American homes 25 years prior. If he simply filed a patent that was a variation of an existing design, that would make his invention not particularly noteworthy, and it is unlikely that anyone would be motivated to write a biography of his life.