But Randolph later admitted to authorities that she left the kids in the auto.
Randolph was charged Friday with two first-degree felony counts of injury to a child causing serious bodily injury.
She said she later broke the auto window to make it look like an accident, the sheriff's office said.
Authorities say a Texas woman told investigators that she left her 2-year-old daughter and 16-month-old son in the hot vehicle where they died last month to teach the girl a lesson, and that they didn't lock themselves in, .
According to the Parker County Sheriff's Office, when asked how long the children might have been exposed to the high temperatures inside the auto, Randolph responded immediately: "No more than an hour".
Authorities were called to the home at about 4 p.m. when the mother said she had discovered them unresponsive in the auto.
The two young children - a 2-year-old girl and a 16-month-old boy - were found dead in Parker County, Texas on May 26.
Medics pronounced both children dead at the scene, authorities said.
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Ms. Randolph was booked into the Parker County Jail on Friday. The investigators involved in the case believe Randolph was exclusively responsible for the death of her two children.
It happened May 26 in Parker County when the mother found her children playing inside the vehicle, according to the Parker County Sheriff's Office.
Those children died last month.
She has been jailed.
This year, 13 children have died nationwide after being left in vehicles, according to noheatstroke.org. She said that she was folding laundry and watching TV when she realized her kids were gone.
When she woke, she went to check on the children and found them unresponsive.
The Texas mom is now in custody at Park County Jail.
In multiple interviews, officials say Randolph created several variations of the events.
Fowler said that any incidents involving any child are hard ones, but this call was especially heartbreaking because of the unfortunate deaths of the two children.