Dehydrated and disoriented, a French couple hiking in the New Mexico heat likely sacrificed themselves to save their 9-year-old son, a sheriff said Friday.

David Steiner, 42, and his wife, Ornella Steinner, 51, died during a hike in hellish heat at White Sands National Monument. But as their water supply quickly dwindled, the Steiners gave their son two sips of water for each one they took, likely saving his life.

The boy was dehydrated but in remarkably good shape when he was found alongside his dead father on a trail, Otero County Sheriff Benny House said.

The father and son were found Tuesday about an hour after park rangers found the mother dead.

"That may be why he fared so well, is he was a lot smaller and probably had twice as much water," House said. "He was well hydrated, compared to the other two."

The boy's name wasn't released. The family was from the small town of Bourgogne, near the city of Reims, France.

The couple appears to have died of heat-related causes, House said. An autopsy to determine the official cause of death was pending, according to the state medical investigator's office.

The family had two 20-ounce water bottles when they set out on the hike along the national monument's Alkali Flat trail at about 1 p.m., House said. The trail is known for crystalline-white sand dunes and ends at the edge of the Alkali Flat, an ancient dry lake bed.

There is no vegetation or shade, and the National Park Service warns summertime visitors to hike only in the cool hours and carry at least a gallon of water per person.

The high temperature at the monument Tuesday was 101, according to the National Weather Service.

House said warning signs were posted in several languages, including French, at the trailhead.

The boy told deputies that his mother began feeling ill and complained of an injured knee about a mile and a half into the hike.

"So she made the decision that you guys go ahead and go on, I'm going to go back to the vehicle," House said. "She made it about a hundred yards before she went down."

He said the father and son were unaware that she was in trouble and continued on the trail, making it about 2,000 feet before the father collapsed.

Park rangers on a routine patrol found the family.

The sheriff's office contacted the French consulate in Los Angeles and officials there notified the family's relatives.

The boy's grandmother flew to Albuquerque and was reunited with him Thursday.

This isn't the first time a heat-related death has occurred at White Sands.

"We have had some fatalities in the years past," White Sands National Park spokesperson Marie Sauter said, according to KFOX-TV. "The most recent one was in June 2011 and that was on the Alkali Flats Trail.

"Folks might come down here and be surprised by the dramatic environment, the trail itself and the extremes in temperature."

The Associated Press contributed to this report.