But it's not just Phoenix, or even the Southwest: It's hot in most of the country.
"It's been steamy from the Gulf Coast all the way to New England, featuring afternoon thunderstorms throughout the region," says CBS News Meteorologist George Cullen.
A week-long heat wave has hit California's San Joaquin Valley, reports CBS News Correspondent Jerry Bowen. One farm worker is dead from heat exhaustion there. And in Los Angeles, three men nearly suffocated in the closed car in which they were sleeping.
Thirteen illegal migrants have died in the Arizona desert in the last four days and the Border Patrol is finding more victims needing help.
Since Saturday, Phoenix police reported a dozen people had died of apparent heat-related illnesses. Ten were homeless; the other two were elderly women, including one whose home cooling system wasn't on.
By comparison, the Arizona Department of Health Services documented 34 deaths because of heat-related illnesses among all Arizona residents last year. The number of illegal immigrants killed by heat-related illnesses are counted separately.
Phoenix has endured above average temperatures every day since June 29, with the high expected to reach 112 degrees on Tuesday. Even during the coolest part of the day, the mercury failed to descend lower than 91 degrees.
The elderly are especially vulnerable.
"It's really awful. It's just taking all my strength," one woman told CBS News.
The spike in deaths prompted the mayor on Monday to ask for water donations. The city has only a two-day supply of bottled water to hand out, reports Bowen.
Bill Manson, development coordinator for Central Arizona Shelter Services, said a number of companies and individuals had been donating water and organizing drives to collect bottled water.
"There's just not near enough shelters," Manson said.
The Catholic Charities of Southern Nevada Summer Day Shelter in Las Vegas, which opened on July 1, has been forced to double its capacity in the last week because of near-record temperatures in the Las Vegas Valley. The director of the shelter, Phillip Hollon, said that because of the heat wave, they have seen "massive numbers" of people.
Will Humble, bureau chief for disease control at the Arizona Department of Health Services, said while homeless people are among those at highest risk from suffering a heat-related illness, most who die every year are people who work outside.
"I don't want to leave people with the impression that homeless people are the only people at risk," he said.
The head of the Presbyterian Church USA says entering the country illegally "should never mean a death penalty."
Church Moderator Rick Ufford-Chase said Christian groups in the area have set up water stations in areas where immigrants have died, and the church groups also are sending out rescue teams to provide food, water and medical care.
Those doing strenuous activity outside can use up to a gallon of water an hour and often also risk depletion of electrolytes, particularly sodium and potassium, even if they are consuming water.
Even those sitting still in the shade need a liter or two an hour, Humble said.
Strangely, another weather problem could help, says Cullen:.
"Some of that moisture could eventually get into the Southwest, which could bring some at least brief relief to that region, but that probably wouldn't occur until the weekend."