Funeral services were held Wednesday for Oliver and Aria Orr

By Chris Harris
Updated June 23, 2016 03:10 PM

The father of the 3-year-old Louisiana twins who died Saturday afternoon after becoming trapped in the sweltering cab of a pickup truck tells PEOPLE he and the children’s mother are “doing the best we can” following the tragedy.

“We are holding up,” Travis Orr, who works as a deputy with the Bossier Parish Sheriff’s Office, says in an interview with PEOPLE. “We are still mourning, so we haven’t been doing any interviews.”

On Wednesday, the twins, Oliver and Aria Orr, were buried following a private funeral service.

Police in Louisiana believe they used a footstool to climb into their father’s unlocked truck. After closing the truck’s door, the two children were unable to free themselves from the vehicle’s stifling cab.

The children’s mother, Alisha, reached out to neighbors to help find the two 3-year-olds after she couldn’t find them. One of those neighbors found them inside the truck at around 3 p.m.

Police say both children were unconscious and not moving. They were transported to a nearby hospital where they were pronounced dead.

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“We’re just doing the best we can right now,” Orr tells PEOPLE before ending Thursday’s interview with a request for privacy.

Autopsies on the Orr twins revealed their deaths were heat-related. No criminal charges have been filed against the children’s parents, but investigators are continuing their investigation into Saturday’s tragedy.

The twins’ deaths come just three weeks after Oliver was released from the hospital after suffering a near-fatal injury, according to police. The boy was in the hospital for over a week for treatment of unspecified injuries.

Ginger Hartman, a spokeswoman for Boone Funeral Home and Crematory in Bossier City, which handled the children’s funeral, describes the service as “very small and very private,” noting only close family members were invited to attend.

“I can’t really say much more than that about the funeral as the family would just really like to keep everything private at this point,” Hartman tells PEOPLE, adding that Oliver and Aria’s deaths hit particularly close to home.

“Handling funerals for children is always hard, but this one really touched me because they were twins – a boy and a girl,” Hartman starts. “I have twins who are male and female so this tragic accident really did touched my heart.”