Steven Dean Gordon, 40, and Preston James Gordon, his 11-month-old son, were killed in the 4:52 a.m. CST fire, Hart County Coroner Jeff Roten said.
Gordon's fiancee, Jamie Kirkendall, 27, and her daughter, Sheyenne Kirkendall, 2, were taken to Caverna Memorial Hospital, then flown by helicopter to Vanderbilt Hospital in Nashville, Roten said.
Kirkendall and her daughter suffered second- and third-degree burns to their faces and hands, Roten said. They were in stable condition Tuesday in the hospital's burn unit.
The fire in the two-story frame house broke out around a wood stove in the living room, Roten said. Only the first floor of the house was occupied.
A fifth resident and friend of the family, Rick Dale Howard, escaped unhurt.
