Portugal has set a new hottest day in May with 40.3C recorded in the central town of Mora, as countries in western Europe grapple with sweltering-hot weather.
The temperature recorded on Wednesday bests Portugal's previous record of 40C set in May 2001.
Ministers in France are meeting to assess the country's preparedness for heatwaves, while tennis number one Jannik Sinner bowed out of the French Open after suffering from the heat. Meanwhile, Italian authorities have issued a red heatwave alert for the capital, Rome, where it could top out at 32C on Thursday.
The heatwave is forecast to continue into the weekend, with Germany, Spain and Switzerland having also faced unusually hot conditions.
Parts of Portugal will peak above 35C on Thursday and Friday before the heat begins to recede, according to the nation's meteorological office.
French Prime Minister Sébastien Lecornu chaired a ministerial meeting on Thursday afternoon to develop a readiness plan for extreme heat events, including combatting forest fires and ensuring adequate water supplies over the summer.
Baccalaureate exams - the French equivalent of A-levels - will continue during the heatwaves, despite some schools having to shut their doors due to inhospitable temperatures inside.
A primary school in Souston, in the Landes region, will remain shut on Thursday and Friday after it reached 53C inside earlier in the week, a local official told French media.
Education Minister Édouard Geffray told BFMTV that exam centres would be able to choose rooms with the most shade, adding that exams would go ahead "simply because the students are prepared and... there is also a schedule according to which they expect their results".
The decision has attracted criticism from education unions and teachers, with one telling French radio of teachers "forced to bring in their own fans".
A survey by France's secondary school union found nearly 78% had recorded temperatures above 30C this week, and said it had received reports of teachers bringing in screwdrivers to prise windows open.
Seventeen departments of France - in the north-west, as well as Paris - are under an orange alert, indicating people should be "very vigilant" about the weather.
Temperatures are expected to reach 33C in Paris on Thursday, and top out at 34C on both Saturday and Sunday.
Police have announced measures to ease traffic in the capital until Saturday, including only allowing lower-emission cars on roads and lowering speed limits. A single fare for the entire public transport network will be offered at the same time.
At the French Open in Paris, Sinner appeared to be cruising to a victory before suddenly taking a turn for the worse.
The Italian complained of dizziness and feeling lethargic before hitting a wall.
"It was a tough spot to be in," he commented afterwards, but added: "Really it was nothing against the heat, nothing against the weather. It was just me today, but it happens."
Meanwhile, Italy's red alert in Rome - as well as in Florence, Bologna, Brescia and Turin - is the first of the year, warning of "possible negative effects on the health of healthy, active people".
Temperatures will climb to 35C in Madrid over the weekend. Though the current spell does not officially qualify as a heatwave in Spain, the nation's meteorological office has said the heat is that usually seen in July and August.
The immediate cause of the heatwave is a "heat dome" - an area of high pressure that becomes "stuck", trapping warm air underneath it.
While it is difficult to link individual extreme weather events to climate change, scientists say climate change makes heatwaves more frequent and more intense.
Over the last 30 years, Europe has been warming by 0.56C per decade, according to the Copernicus climate service - enough to make heat extremes significantly more severe.
The UN warned on Thursday that global average temperatures are likely to continue at or near record levels this year and for the next four years.
The 11 hottest years ever recorded all happened from 2015 onwards, and the UN's weather and climate agency said this trend was predicted to continue, with a new hottest-ever year "likely" before 2031.
