In many areas the thermometer showed slightly lower temperatures than in recent days but there were warnings that the relief might be temporary.
In France, medical authorities said 22 people have now died from the heat -- up from nine two days ago. They included a child of 15 months, four labourers and two homeless people.
The updated count brought to 31 the number of people who are believed to have died since the start of the week in western Europe, including two new victims reported in Spain.
National radio started broadcasting messages to the elderly Saturday, explaining the effects of the heat and how to combat them and giving a telephone advice-line number.
French forecasters have placed the eastern half of the country on "orange" alert -- the second highest level -- warning of more peaks at the weekend. Temperatures were expected to reach 38 degrees Celsius (100 degrees Fahrenheit) in the Rhone valley, though cooler weather was forecast for Sunday.
Violent storms struck the Dordogne region of south-central France overnight, killing a motorcyclist who ran into a fallen tree. Scores of firemen were mobilised and lightning caused half a dozen forest fires.
Authorities in Budapest are distributing water in some of the most frequented areas of the city to keep people from dehydration.
Trains on several routes across the country have been ordered to lower their speed owing to problems with the tracks caused by heat.
In Britain forecasters warned that the present relief, welcome after Wednesday -- which saw the hottest July day on record -- was likely to be followed by another heatwave next week.
"We will have another heatwave similar to this week," said forecaster Steve Randall from the Meteorological Office.
"The weekend will be cooler with a risk of thunderstorms -- but temperatures will still be above average for the time of year."
Those with inclination and the money, a newspaper reported Saturday, could cool off with a luxury ice-cream -- a cone costing a chilling 30 pounds (44 euros, 55 dollars).
In Italy temperatures were set to reach 40 C over the weekend, and the regions of Liguria in the northeast and Umbria in the centre were placed on the highest level of alert.
In Berlin the building union IG Bau launched a publicity campaign under the slogan "Don't Get Burned", and distributed tubes of sunscreen cream at work-sites.
In the Czech Republic a mediaeval clock in Prague which is one of the city's top tourist attractions is running slow because of the heat, the authorities said.