The boy was left tied to the tree until the following afternoon when his stepmother found him unresponsive, Sheriff James Knight said. Knight said authorities believe the boy was bound to the tree with plastic ties and possibly other kinds of material.
"An adult couldn't get out of those," he said.
Temperatures in the area rose to above 90 degrees on Thursday afternoon, with a low of 73, according to the National Weather Service. Knight would not discuss any details on the cause of death, saying an autopsy was being conducted at the state chief medical examiner's office in Chapel Hill.
The sheriff also didn't have details on why the boy was being punished, although he said deputies were investigating whether he had run away.
Dwight Jefferson, an emergency responder with Pinetops Rescue Squad who was first on the scene, said he did not know the cause of the child's death.
"What we found was a 13-year-old laying on the ground -- CPR being done by his father," Jefferson said. "Then we took over."
Knight said the boy was taken to a local hospital where he was pronounced dead.
McMillan and Sandra Elizabeth McMillan, 36, also have been charged with felony child abuse. Two other children at the home, ages 7 and 9, have been placed in the custody of the Department of Social Services, authorities said. Knight said he does not know of any past allegations of child abuse in the family.
He also said he could not release the name of the boy.
The McMillans are being held in the Edgecombe County Detention Center under no bond and are scheduled for a first appearance in court Monday. The sheriff's office said they did not know if the couple had an attorney.
Macclesfield is about 90 miles east of Durham.
