The high temperatures that have scorched Europe for the past two weeks are unlikely to drop until mid-August, forecasters say.
Millions across Europe are seeking refuge from searing temperatures
Temperatures across the continent have regularly exceeded 40 degrees Celsius (104 Fahrenheit).
The number of deaths blamed on the heatwave reached 39 on Saturday.
Fires fuelled by hot winds have destroyed woodland from Portugal to the Netherlands and Greece.
In the Paris area - where temperatures are on a par with Mecca in Saudi Arabia - firefighters say they are dealing with 600 calls every day for people suffering from the heat.
Paris department stores reported a run on portable electric fans as people desperately sought refuge from the scorching weather.
One of the city's tourist attractions, the Catacombs, has been turning away visitors - such is the demand for the chill inside.
In Britain, tourists were disappointed when the London Eye - a big Ferris wheel on the bank of the Thames river - remained closed because of heat that would have made the glass capsules unbearable.
Zurich revelled in the heat at the city's annual street parade
However the heat wave did not halt the annual Street Parade in Zurich, Switzerland, where scantily-clad revellers danced to one of the world's biggest techno-music parties.
German TV reported on Friday a temperature of 40.8C in the western Saarland region - the hottest since records began in 1901.
In Italy, the state-funded CNR research centre said the weather conditions
would probably continue into September and described the heat wave as one of the five worst in 150 years.
In Romania, the authorities say the wrecks of two Nazi ships that sank in the Danube during World War II recently resurfaced.
Summer fires have destroyed around 175,000 hectares (430,000 acres) of pinewood and brush across the continent, most of it in Portugal.
However Portuguese firefighters say they have almost brought the blazes under control.
Wildfires are still raging in Spain, Croatia, Greece, the Netherlands, Italy, and France.
French police have arrested five suspected arsonists in connection with a forest fire that broke out near the southern city of Nice on Friday.
The extreme heat is being partly attributed to intense monsoon activity in sub-Saharan Africa which has poured hot desert air over Europe while keeping out cooler Atlantic lows.
The BBC's environment correspondent, Tim Hirsch, says this week's weather fits a global trend which has seen previous records shattered with increasing regularity.
In nine out of the past 12 years, average temperatures worldwide have been higher than at any time since records began in the 19th century and it is very likely that the 1990s were the warmest decade for 1,000 years.