In London, a new British heat record for the month of May was measured for the second day in a row - 35.1 degrees in Kew Gardens in the western part of the capital.
At least five weather-related deaths have been reported in the country since the weekend - four of them involving teenagers and all of the victims drowned, reports the BBC.
The heat also causes disruptions to train traffic and fires have broken out in several places, Sky News reports.
Ireland is also hot. During the day, a record high of 30.5 degrees was measured outside Limerick, reports RTE. The 32.3 degrees measured in Cardiff is also a May record for Wales, according to the BBC.
Over 40 degrees?
France set 400 local monthly records on Tuesday, with the weather agency Météo-France reporting that the average temperature during the day was 24.8 degrees, a new record for the month of May. And the country can expect even higher local temperature peaks in the coming days, between 38 and 39 degrees - or more.
"We cannot rule out temperatures of 40 degrees, but if they are reached it would be extremely local," says Adrien Warman at Météo-France to Le Parisien, pointing out Languedoc in the southeastern part of the country as the worst affected by the heat.
Seven deaths have been confirmed in the country in recent days with a direct or indirect link to the heat, government spokesperson Maud Bregeon told TF1. Most of them were drowning.
To give the capital's residents a little more space to spend time in cool environments, the Paris municipality has extended the opening hours of 14 parks.
Heat dome
In Spain, temperatures are also expected to reach 38 degrees later in the week, and in some parts of Italy restrictions have been imposed on outdoor work.
The current heat wave is due to a heat dome, where warm air from northern Africa has been trapped under a strong high-pressure area.
Human-caused climate change is making extreme weather events such as heatwaves, droughts and floods more intense, and Europe is warming faster than the global average.
