Randolph, 24, went to check on her children after about a half-hour - but they were "gone," she told police. She said that after a half-hour of searching, she finally spotted their bodies, unresponsive, inside her 2010 Honda Crosstour parked in her driveway.
It was May 26, a day when the high temperature outside Randolph's home in Weatherford, Texas, reached 96 degrees, according to police records.
Medics pronounced both children dead at the scene, authorities said.
According to the Parker County Sheriff's Office, when asked how long the children might have been exposed to the high temperatures inside the car, Randolph responded immediately: "No more than an hour."
Less than a month after the tragedy, Randolph has been arrested after her original explanation for her children's deaths unraveled. Through multiple interviews with investigators over the past month, Randolph "created several variations of the events" of May 26, police said.
In a final interview with investigators Friday, Randolph described an entirely different timeline for what happened that day - one that began much earlier in the afternoon than she had previously admitted.
At about 12:15 p.m., Randolph said she had found her children playing inside her car and ordered them to come out, police said.
"Stop your s-t," Randolph said she told her 2-year-old daughter, according to police.
"When they refused to exit, Randolph told police she shut the car door to teach Juliet a lesson, thinking she could get herself and her brother out of the car when ready," a probable cause affidavit for the incident stated. "The defendant went inside the house, smoked marijuana and took a nap. The defendant said she was asleep for two or three hours."
Randolph was charged Friday with two first-degree felony counts of injury to a child causing serious bodily injury. She is being held at the Parker County Jail on a $200,000 bond, records show. A sheriff's spokeswoman did not immediately return a call Saturday afternoon, and jail records do not list an attorney for Randolph.
Over the past two decades, more than 700 children have died of heatstroke while in hot cars, said Jan Null, a meteorologist who compiles and keeps track of the data on noheatstroke.org.
"Every one of these can be prevented," Null told The Washington Post last year.
Null said more than half of the incidents occurred because a child had been "forgotten" by a caregiver. About 28 percent of those deaths were because a child had been playing in an unattended vehicle. About 17 percent of the deaths resulted because a child was intentionally left inside a vehicle by an adult, Null's site states.
The National Safety Council says that unintentionally leaving a child inside a car "can happen to anyone."
"Maybe it's an overworked parent who forgets to drop off their child at day care, or a relative who thinks the child will be okay 'for just a few minutes,' " says an NSC pamphlet on the issue.
The group advises parents to put something they will need by their child's car seat - a purse, wallet or phone, for example - as an additional reminder to check the back.
"Remember, children overheat four times faster than adults," says a message on the council's website. "A child is likely to die when his body temperature reaches 107 degrees, and that can happen in minutes."
Those who see a child alone in a car are advised to call 911 immediately or even break into the car during an emergency, the group said, noting that many states have good Samaritan laws.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)