Firefighters battled blazes in parts of Greece and the Canary Islands while Spain issued heat alerts and some children in Italy's Sardinia were told to stay away from sports.
From California to China, authorities warned of the health dangers brought by searing temperatures, urging people to drink water and shelter from the sun.
"You can't be in the street, it's horrible," said Lidia Rodriguez, 27, in Madrid.
Temperature records tumbled around the world, with new heat streaks set in China and the United States, and fresh highs in France.
Beijing broke a 23-year-old record with 27 consecutive days of temperatures above 35 degrees Celsius (95 Fahrenheit), forecasters said.
Phoenix broke a similar record, in place for 49 years, with its 19th consecutive day of temperatures of 43.3 Celsius or higher, weather officials said.
In southern France, a record 29.5C was recorded in the Alpine ski resort of Alpe d'Huez, while 40.6C had been recorded for the first time in Verdun in the foothills of the Pyrenees.
In a stark reminder of the effects of global warming, the UN's World Meteorological Agency (WMO) said the trend showed "no signs of decreasing".
"These events will continue to grow in intensity, and the world needs to prepare for more intense heatwaves," John Nairn, a senior extreme heat adviser at the WMO told reporters in Geneva.
- Heatwave on horizon -
Northwest of the Greek capital Athens, columns of smoke loomed over the forest of Dervenohoria, where one of several fires around the capital and beyond was still burning.
Fire spokesman Yannis Artopios called it "a difficult day", with another heatwave on the horizon for Thursday, with expected temperatures of 44C.
A forest fire by the seaside resort of Loutraki, where the mayor said 1,200 children had been evacuated Monday from holiday camps, was still burning.
In the Canary Islands, some 400 firefighters battled a blaze that has ravaged 3,500 hectares of forest and forced 4,000 residents to evacuate, with authorities warning residents to wear face masks outside due to poor air quality.
Temperatures were unforgiving in Italy and in Spain, where three regions were put under hot weather red alerts.
The Italian islands of Sardinia and Sicily have been forecast to possibly surpass a continent-wide record of 48.8C recorded in Sicily in August 2021.
At Lanusei, near Sardinia's eastern coast, a children's summer camp was restricting beach visits to the early morning and forbidding sports, teacher Morgana Cucca told AFP.
In the Sardinian capital of Cagliari, pharmacist Teresa Angioni said patients were complaining of heat-related symptoms.
"They mainly buy magnesium and potassium supplements and ask us to measure their blood pressure, which is often low," Angioni said.
Many throughout Italy sought escape by the sea, including outside Rome, where the midday heat hit 40C.
"Certainly it's better at the beach, you can at least get a little wind from the sea. It's not even possible to remain in the city, too hot," said Virginia Cesario, 30, at the Focene beach near the capital.
- Climate change impact -
Tens of millions of Americans experienced dangerous heat levels on Tuesday.
In the town of San Angelo, Texas, where temperatures were expected to reach 104-108F (40-42C), the National Weather Service said it was "running out of ways to say that it's gonna be hot out there today."
"With temperatures across the area likely topping the 105 mark yet again, we implore you to continue to practice heat safety and try to stay cool," the agency said on Twitter.
And in Arizona, the mercury at Phoenix Sky Harbor Airport again reached 110F on Tuesday, breaking the previous record of 18 consecutive days at or above that temperature, set in 1974.
The heat waves across Europe and the globe are "not one single phenomenon but several acting at the same time", said Robert Vautard, director of France's Pierre-Simon Laplace climate institute.
"But they are all strengthened by one factor: climate change."
The record-setting heat came as US climate envoy John Kerry met with Chinese officials in Beijing, with the world's two largest polluters reviving stalled diplomacy on reducing planet-warming emissions.
Speaking Tuesday at Beijing's Great Hall of the People with China's top diplomat Wang Yi, Kerry called for "global leadership" on climate issues.
burs-mca/cwl
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