He later died at the UC Davis hospital burn center in California, the sheriff says.
Friday's high temperature, recorded nearest to Burning Man, was expected to hit 98, he said, while Saturday and Sunday could get to 101, and Monday 100.
Mitchell was a USA citizen from Oklahoma but was now living in Switzerland.
The box reportedly arrived at Google's Sunnyvale offices on August 21 and was then driven two days to Black Rock City, Nevada, where Burning Man took place.
Some 70,000 people from all over the world are thought to attend the gathering, and the man is believed to have dodged a number of security personnel to reach the flames.
"The nine-day festival in northern Nevada was briefly hampered when a lightning-sparked wildfire temporarily shut down Burning Man's main travel route last week", according to SFGate.
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Jim Bourg / Reuters Firefighters are forced to abandon their attempted rescue of a Burning Man participant who ran into the flames of the "Man Burn" when the structure began to crumble and fall around them.
Organizers are also offering emotional support counseling on site, saying in a statement: "Now is a time for closeness, contact and community".
That's because the free-wheeling, don't-call-us-a-festival dedicated to radical self-expression and reliance in the middle of nowhere is nearly 4,000 feet above sea level.
As of this morning, Pershing County Sheriff Jerry Allen confirmed that man had died from his injuries.
Of note, reports told of previous attendees in years past having attempted to elude security detail attempting to gather pieces of the spectacle as a token and going through the hot coals.