For their anniversary road trip through the West, an escape from the humid misery of a Louisiana summer, Tyson and Adeline Maddox rented a glimmering convertible.

They have kept the top on. It has been too hot to do anything else.

“Reminds me of the engine room,” Mr. Maddox grumbled of the weather as he left the “Welcome to Fabulous Las Vegas” sign on Wednesday evening, when temperatures were still well into triple digits.

“The heat, it’s just constantly coming,” Ms. Maddox added later. “It’s like being in front of an exhaust pipe.”

So it has been around the Las Vegas area this week. Pedestrians sometimes felt scarcer than jackpots. Playgrounds stood empty and silent. Merely walking through a parking lot meant squinting — not at the sunlight blanketing the region, but at a heat so punishing that eyes hurt without ever actually watering.

At times, the mercury’s ticks upward have come so fast that forecasters, at once awe-struck and unnerved, could hardly keep up.

“Remember 20 minutes ago when hitting 117°F was a big deal?” the local National Weather Service office wrote on social media on Wednesday. “Well, the airport hit 118°F.”

Thursday was not shaping up to be much of a reprieve, at all.

More than 60 million Americans were under heat alerts from the National Weather Service on Thursday, as a searing heat wave that has engulfed the West for more than a week continued to blister the region. Dangerously high temperatures are forecast to last there through Saturday, and shift east to the central and eastern U.S. by Sunday.

In southeast Texas, where Hurricane Beryl left millions of residents without power on Monday, people sweltered without air-conditioning and hospitals were “backed up” because doctors were wary of discharging patients to homes without power, officials said Wednesday.

By Thursday morning, more than 1.1 million CenterPoint Energy customers were still without electricity. The company said that it hoped to get the lights back on for 400,000 customers by the end of Friday, but that about 500,000 customers would probably still be without power into next week.

Across the West, large parts of California, Nevada, Arizona and Utah were under excessive heat warnings, indicating “extremely dangerous heat conditions.” Officials believe heat may be to blame for more than 90 deaths reported in the West this month, though it could take months of investigations for the authorities to determine an accurate death toll.

More than a dozen high-temperature records were expected to fall on Thursday, from the West Coast to the High Plains, where temperatures will soar from the upper 90s into the triple digits. Some places in the deserts and interior valleys of California, Arizona and Nevada will once again hit the 110s and 120s.

The Las Vegas Valley, home to about 2.3 million people, is under an excessive heat warning that runs until Friday night. Wednesday was the fifth straight day that the daytime high reached or exceeded 115 degrees, a record.

Overnight, the temperature dipped to 93 degrees, which Morgan Stessman, a Weather Service meteorologist, said was the highest low ever recorded on July 11.

By about 4 a.m. on Thursday, a car’s thermometer, questionable as it might be, reported that it was 107 degrees outside. The official reading at that hour was 97 degrees at Harry Reid International Airport, according to the Weather Service, headed for a projected afternoon high of about 118 degrees, which would be a record for July 11. Before this week, it would have broken the city’s all-time record, too.

“Right now, it’s just a matter of getting inside, being smart as far as hydrating yourself, and just living your life as well as you can,” said Oscar Goodman, who moved to Las Vegas in 1964 and later served as mayor for 12 years, before he relinquished the job to his wife. “Thank God we have enough air-conditioning here that people are comfortable — once they get inside, of course.”

An irrepressible bettor, Mr. Goodman said that he had tried without success to persuade the city’s books to accept a wager on how high the temperatures would get during this heat wave. He would not confess whether he was joking — for good measure, he threw in a reference to the city’s history with organized crime — but he said that he never remembered Las Vegas feeling so hot.

This summer has given residents some time to get used to the heat, even as they have complained while walking to restaurants and shops in parts of Clark County away from the Las Vegas Strip.

It has not been so simple for visitors like the Maddox family. So they have largely tried to stay inside, where air-conditioners rumble and strive to tame the temperature toward something tolerable.

Las Vegas was not the Maddoxes’ original ambition: They had planned to visit the Caribbean, until Hurricane Beryl unleashed havoc there. With a week off work already arranged, they resolved to travel someplace anyway. Now, they have heard no shortage of feedback from Louisiana, which has seemed mild by comparison.

“Everybody back at home is saying, ‘You’re crazy, You went out there in July!’” Mr. Maddox said.

He shrugged. Then he fished in his pocket for the rental car’s key fob. He wanted to start the air-conditioning before he got to the convertible.