A man in Las Vegas is believed to have died from a heat-related illness.
Air-conditioned “cooling centres” have been set up in California, Nevada and Arizona, as officials warn the heat could be life-threatening.
Temperatures in some areas are expected to be near 130F (54C) – close to the world’s all-time record.
Several parts of California – including the desert town of Palm Springs – saw record highs on Saturday.
There are fears of wildfires, as the heat could last for several days.
More than 34 people were taken to hospital after attending an outdoor concert in Las Vegas, Nevada, officials said.
They also said that an elderly resident was found dead in a house with no air-conditioning. The man suffered medical problems, but his condition is believed to have been aggravated by the heat, according to the Associated Press news agency.
In Los Angeles, California, a number of people were treated for heat stroke and dehydration.
Shelters for homeless in Phoenix, Arizona, added extra beds as temperatures in the city were expected to hit 122F (50C).
The Running with the Devil Marathon in the Mojave Desert outside Las Vegas – which had been scheduled for Saturday – was later cancelled because of extreme heat.
The National Weather Service earlier issued a heat warning for several parts of the region until Monday morning.
Temperatures in Death Valley in the California desert are forecast to reach 130F (54C). The highest-ever temperature on Earth -134F (56.7C) – was recorded there on 10 July 1913.
The heat wave comes after one of the driest winters on record, and there is a fear of wildfires.
Energy suppliers are expected to be pushed to the limit in the next few days.
Weather officials say the extreme weather is caused by a high-pressure system stuck over the area.
The US Border Patrol’s rescue unit has added extra personnel this weekend as the threat of exhaustion and dehydration rises for those attempting to cross the US-Mexico border illegally on foot.
At least seven migrants were found dead in Arizona’s desert last week in lower temperatures. Border officials in Tucson, Arizona, rescued more than 170 people suffering from the heat during a thirty-day period in May and June.
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