Coryell County Justice of the Peace Jimmy Wood says the boys, whose names were not immediately released, died five days short of their third birthday.
Officials say the twins sometimes slept in the portable building that was once used mainly for storage.
Vaden says the children's mother and boyfriend were in a mobile home nearby.
The cause of the blaze hasn't been determined. The county sheriff's department, Texas Rangers and state fire marshal are investigating
The children's bodies were sent to Dallas for autopsies.