The body of Jonathan Gerrish, 45, from Lancaster, was found in Devil's Gulch Valley, deep in the Sierra National Forest in August - along with his American partner Ellen Chung, 30, their one-year-old daughter Aurelia Miju Chung-Gerrish and the family's dog Oski.
Their unexplained deaths had puzzled police in the US, with the Mariposa County Sheriff's Office ruling out a number of possible causes over the past two months.
Concerns over water quality in the nearby Merced River led to speculation that an algae bloom could have killed them, but officials say there is no evidence that the family drank the river water.
Other dismissed theories included a leak that originated from abandoned gold mines that are common in the Gold Rush region.
But in a news conference on yesterday (Thursday, October 21), it was revealed that the family had been found with an empty 85oz (2.5-litre) water bladder and did not have any other bottles or water filters with them.
Temperatures on the day of their hike rose above 109F (42C), say police, and this evidence has led investigators to conclude that they family died due to hyperthermia.
"For Mariposa County, this is rare," said Jeremy Briese of Mariposa County Sheriff's Office. "This is the first hyperthermia cause of death that I've witnessed here in 20 years."
He added that there is no phone service in the area where they were hiking, and that an earlier fire had burned trees that would normally provide shade in some sections of the steep trail.
US news station CBS said Mr Gerrish, who is from Lancaster and has family in Bamber Bridge, met Ms Chung in San Francisco before moving to the small town of Mariposa in 2020.
Their bodies were discovered by rescue crews on August 17 in an area south-west of Yosemite National Park after a friend reported them missing.
The Mariposa County Sheriff's Office has been working with the FBI, environmental researchers and toxicologists to determine what killed the family.
Police confirmed the bodies showed no sign of trauma and no suicide note and they had already ruled out death by lightning, carbon monoxide, carbon dioxide, cyanide, illegal drugs, alcohol, gun "or any other type of weapon".
CBS News added that the FBI is still attempting to access the mobile phone owned by Gerrish, who was a software developer for Snapchat and had previously worked for Google.