West Licking Fire Chief Jim Weber said a kerosene heater was out of fuel in the unfinished room where the men were found wearing winter coats, and the only vent was an open window in the basement.
A fourth worker was taken to a hospital in critical condition.
Firefighters received a 911 call reporting four people were possibly frozen in a room of a house in the new subdivision about 17 miles east of Columbus, where temperatures dipped to 32 degrees overnight.
Only one of the men, who were in their late 20s to early 30s, was authorized to work on the house, Pataskala police Chief Chris Forshey said. That worker, a drywall installer, was among the dead.
Authorities said two of the men had identification cards saying they were from Mexico.
The house's builder, Jefferson Homes, and a construction foreman on the site Monday declined comment.
