The Czech Republic recorded its highest-ever temperature on Saturday, with a reading of 40.8C at a weather station in Doksany north of Prague, the national meteorological service (CHMI) said.
And forecasters in Denmark said a provisional temperature of 37C was recorded in Odum, near Aarhus. This exceeded the previous all-time record of 36.4C set in 1976.
Switzerland broke the record for its hottest-ever June day for the third day in a row on Saturday, with the mercury rising to 39C in the northern city of Basel.
“This exceptional heatwave has been caused by a slow-moving persistent area of high pressure, a so-called ‘heat dome'”, according to the BBC’s lead weather presenter Ben Rich.
“Underneath the high pressure system sinking air compressed and warmed, lifting temperatures day by day.
“The skies have remained largely cloud-free, allowing strong sunshine to heat things up even more”, he added.
Since the heatwave began, the number of drowning deaths in France has risen to at least 55. An estimated two-thirds of them had been swimming in unsupervised areas.
Spain’s MoMo monitoring system has recorded 327 deaths that could be linked to the heat between Sunday and Thursday.
Europe is the World’s fastest-warming continent – because of a range of factors including the rapid heating of the Arctic, and changes in the pattern of the jet stream.
Scientists from the World Weather Attribution say a heatwave of this magnitude so early in the summer would have been virtually impossible 50 years ago.
They say climate change is “unequivocally” to blame.
The extreme heat will continue over the weekend into Monday with temperatures above 40C still possible in places, says BBC weather forecaster Ben Rich.
However cooler conditions developing in the west of the continent will sweep eastwards to bring some relief later in the week.