He then flew out of the city for a business trip, police said.
His wife, Jenny Barker, left for her job in another vehicle thinking that both children were at the day-care center, police said.
Outside temperatures in the area reached 31 degrees and it is believed to have been much hotter inside the truck. Police said that as she pulled into the driveway at the home on Virginia Avenue, she dialed 911.
She pulled the baby out of the auto and began performing CPR until paramedics arrived. Children's Hospital at Vanderbilt, in Nashville.
Barker and his wife have been fully cooperative with the investigation.
The incident occurred outside this property in Virginia Avenue East Nashville
Tennessee ranks eighth in the nation in child hot vehicle deaths. There have been 30 children who have died since 1990.
Investigators say the girl's mother found her inside the the pick-up truck Wednesday night.
Her adoptive mother found the infant in the truck at the family's home Wednesday evening.
Metro Nashville police in Tennessee said little girl's adoptive father reportedly forgot about the child after dropping off her sibling at daycare. It's not clear how long the girl was in the truck.
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