Temperatures in Bordeaux in southwest France were forecast to exceed 42C on Monday and weather agency Meteo France said 49 regional administrative areas would be under a red heatwave warning.
"We're heading for, at the very least, several days of very, very hot weather," French Health Minister Stephanie Rist said on TV channel TF1.
"We don't know when temperatures will start falling."
Three elderly people, aged between 80 and 95, died at the weekend in the Bordeaux region as a result of health issues caused by the current heatwave in France, local government official Sophie Brocas told France TV late on Sunday.
In Spain, state weather agency Aemet issued a red alert for the Basque country, in the normally cooler north, with the mercury in San Sebastian set to rise to a high of 40C, more than double its historic average for June 22, according to the Reuters Climate Monitor.
San Sebastian was set to be hotter than the southern cities of Seville and Cordoba, which normally record the country's most intense summer heat.
"We are seeing temperatures between five and 10 degrees above normal for this time of year, and in some northern areas even more than 10 degrees above average," Aemet spokesman Ruben del Campo said.
The night was providing little relief in some parts of Spain, with temperatures failing to drop below 25C or even 30C in places like the southwestern province of Almeria, Aemet said.
Europe on Monday was the continent furthest from its historic norm, with an average high temperature of 24C, which was 4.1C above what was typical from 1961 to 1990, according to the climate monitor.
By comparison, Asia and North America were 2C and 1.3C above the historic norm.
Wildlife shelters in northern Europe were struggling to cope with the number of animals being brought in suffering from the heat.
Birds such as swifts, swallows, sparrows and starlings, which make their nests in the eaves of roofs, have been particularly affected by abnormally high temperatures, said Romaine de Jaegere, a biologist and founder of the Centre for the Rehabilitation of Animals Living in the Wild (Creaves) wildlife refuge in Temploux in Belgium.
"Temperatures on the roofs can sometimes reach 50, even 60 degrees Celsius. So they prefer to jump rather than let themselves die and literally cook in their nests," De Jaegere told Reuters, adding that the shelter had received 150 animals in three days.
Spain's Labour Ministry on Monday said it was monitoring whether companies were complying with laws that allowed workers to reduce or adjust their hours when orange or red weather alerts are issued.
Workers are also entitled to up to four days of paid leave if they are unable to reach their workplace due to weather conditions, it said.
