The children, a boy and a girl, were found two hours after being reported missing on Sunday near Topeka. The children, whose names were not released, were found inside the vehicle parked in the driveway of the home.
The Topeka Capitol-Journal reports that sheriff's deputies performed CPR on the children, but to no avail.
A spokesman for the Shawnee County Sheriff's Department, Sgt. Jay Simecka, said officials initially thought the children were twins, but after checking birth records they discovered that the girl was born Sept. 29, 2004, and her brother Aug. 2, 2005. No other details were immediately available.
Simecka said the county coroner was still doing a preliminary investigation. Authorities also were trying to assemble an accurate timeline of events and determine how the children ended up in the car.
"We will know something more in the next day or so," he said, adding that a news conference was scheduled for Monday afternoon.
Sgt. Akim Reynolds on Sunday said that the boy was found in the front seat of the car. The girl was found in the back seat.
The girl was pronounced dead at the scene. The boy was pronounced dead at a hospital.
Reynolds says the doors to the car were unlocked.
"The officer who opened the door said it was very hot inside the car," Reynolds told The Capital-Journal.
The temperature was about 75 degrees. Reynolds said the temperature inside a car with its windows up could be 20 to 30 degrees warmer.
The mother was being questioned by detectives. The child's father, whom Reynolds said worked out of town, had been notified and was returning to Topeka.