Firefighters battled blazes in parts of Greece and the Canary Islands, Spain issued heat alerts while some children in Italy's Sardinia were warned away from sports for safety reasons.
"You can't be in the street, it's horrible," said Lidia Rodriguez, 27, in Madrid.
From California to China, authorities have warned in recent days of the health dangers of the extreme heat, urging people to drink water and shelter from the sun.
Several local temperature records were broken in southern France, the weather service said.
Meteo France said a record 29.5 C (85 F) had been reached in the Alpine ski resort of Alpe d'Huez, which sits at an altitude of 1,860 metres (6,100 ft), while 40.6 C 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 of heatwaves "shows 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 advisor at the WMO told reporters in Geneva.
Wildfires and scorching heat
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 44 degrees Celsius (111 degrees Fahrenheit).
Still burning was a forest fire by the seaside resort of Loutraki, where the mayor said 1,200 children had been evacuated Monday from holiday camps.
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 on watch to possibly surpass a continent-wide record of 48.8 degrees Celsius, recorded in Sicily in August 2021.
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
The heatwaves 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."
Health authorities in Italy issued red alerts for 20 cities, from Naples in the south to Venice in the north.
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.
Heat record in China
In parts of Asia, record temperatures have triggered torrential rain.
Nearly 260,000 people were evacuated in southern China and Vietnam before a typhoon made landfall late Monday, bringing fierce winds and rain, but weakening to a tropical storm by Tuesday.
China reported on Monday a new mid-July high of 52.2C in the northwestern Xinjiang region's village of Sanbao, breaking the previous high of 50.6C set six years ago.
The record-setting heat came as US climate envoy John Kerry met with Chinese officials in Beijing, as the world's two largest polluters revive 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.