Weekend temperatures could also hit 40C in the Austrian capital Vienna, and a code red comes into effect in eight out of 12 provinces in the Netherlands from midnight on Thursday local time, with the chance of 39C in localised eastern areas.
The UK’s Met Office has extended its red extreme temperatures warning until Friday evening, for parts of London and south-eastern England.
In Italy, Florence’s Uffizi museum has halted ticket sales until 28 June, and only those with a previous booking will be allowed in.
Management said the air conditioning system could not cope with the high flow of visitors and the extreme temperatures, which reached 32C inside the museum on Wednesday.
Italians have been experiencing high temperatures since the start of this week – but the peak of the heat is expected for Monday, when 40C are expected in various northern regions.
Night-time temperatures in those areas might not drop below 29C.
“Gone are last century’s June days of 32C daytime temperatures and cool 17C nights,” forecaster Lorenzo Tedici told Italian media.
“We have become so accustomed to excess that, paradoxically, today we welcome a forecast of 34C as good news.”