They say Cynthia Marie Randolph has admitted she shut the door to teach her two-year-old daughter Juliet a "lesson" after she had refused to leave the car.
BBC reports Juliet and her 16-month-old brother Cavanaugh were pronounced dead at about 16:30 on 26 May.
Temperatures outside at that time were about 96F (35.5C), police say.
The incident happened at Ms Randolph's home near Lake Weatherford, the Parker County Sheriff's office says.
