Meteorologists have said that the episode is due to scorching-hot air blowing in from the Sahara desert.
Climate experts have said that such heat waves early in the summer are likely to become more frequent as the planet heats up.
Fearing the smog that Paris is especially prone to during stretches of hot weather, city authorities have banned older models of diesel and petrol cars from the city on Wednesday. Parisian drivers are also being offered free parking places to encourage them to use public transportation instead.
As part of its emergency heat plan, the city opened 34 cool rooms in public facilities with air conditioning, and a hotline for elderly or vulnerable people who need assistance reaching their nearest public cool room. Eighteen public parks will stay open 24/7. Many public pools and the pond of the Bassin de la Villette will be open to swimmers until 10:30 pm each evening this week.
Authorities are taking no chances in France, where a heatwave in August 2003 was blamed for 15,000 deaths. In an unusual move, French education minister Jean-Michel Blanquer on Monday postponed national school exams to next week. Fifty-one schools in the region around Paris were already closed for the day by midday Wednesday, and more are expected to close this week.
The heat wave is gripping France as the French Parliament hotly debates new legislation on energy and climate, which has been heavily criticized by opponents for not being ambitious enough. The bill aims to turn France carbon neutral by 2050 but postpones for ten years the former goal to cut the nation's nuclear energy use by half.
In Germany, more than 16 acres of forest in Grunewald near Berlin fell victim to fire on Tuesday. Authorities also fear car tires exploding from the heat on the road, and have imposed new speed limits on drivers on Germany's famously speed-limit free motorways.
In Lithuania, six people drowned seeking relief from record heat in rivers and lakes in the north of the country.
The heat wave is set to affect all of western Europe, particularly France, Italy, the United Kingdom, Austria, Switzerland, the Netherlands and Belgium. The highest temperatures are expected on Thursday and Friday.