Southern Spain, southwest France and northwest Italy all recorded temperatures of more than 35 degrees Celsius and a vast swathe of the continent from the west coast of France into Poland sweltered in temperatures of 30-35 degrees.
France’s public health body InVS announced that the heat had claimed the lives of "about 40" people and an estimated 10 people have died elsewhere in Europe.
In 2003, a similar heatwave killed tens of thousands of people, including 15,000 in France.
European governments and medical services have stepped up their efforts to prevent deaths this time, urging people to drink water, keep cool and look out for elderly citizens who are particularly at risk.
Temperatures were expected to peak Wednesday or on Thursday in France, Britain and Germany before cooling off around the weekend with stormy conditions expected in some areas.
Isolated storms erupted on Tuesday causing a mini-tornado in the northern Italian city of Turin and knocking out telephone lines in southwest France.
Electricity outages across US
In the United States, Americans are sweating out a heat wave that has caused major power outages from coast to coast.
Power shortages were reported in California, Missouri and New York, with the mercury hitting an unprecedented 48 degrees Celsius over the weekend in Woodland Hills, part of the sprawling Los Angeles metropolitan region.
The Los Angeles Times reported 13 heat-related deaths in California's Central Valley and four in southern California, mostly among the elderly.
For two days now power outages stretched up the Pacific Coast, from Los Angeles in the south to San Francisco to the north and into California's Central Valley.
"This is clearly a historic weather pattern that we have not seen in 57 years," said Joe Desmond, undersecretary of energy affairs at the California Resources Agency.
"Voluntary conservation is making the key difference right now," he said.
California has a population of 36.1 million. Electricity demand hit a record 50,538 megawatts on Monday.
The heat knocked out the Los Angeles-based servers for the US’s most popular website MySpace for several hours on Monday.
The company said the web site was offline after an area power outage and a backup generator failed.
California’s fire threat
According to officials heat also helped a fire in a southern California forest to double in size over the past 24 hours, scorching some 6,000 hectares.
The California Department of Forestry (CDF) reported that the blaze, which spread through the Cleveland National Forest 65 kilometers east of San Diego, was ignited on Sunday by a campfire.
"As the day heats up, we expect the same parts of the fire to come to life," spokeswoman Roxanne Provaznik said.
Meanwhile, in the Midwestern state of Missouri, 159,000 people remained without electricity amid boiling heat and humidity in the wake of two thunderstorms that hit the region over the past week and shut down power supplies.
In New York City, at least 6,000 people and 750 businesses in the Borough of Queens have been without electricity for nine days.
Concern for European farmers
Farmers in France, the Netherlands and Poland have already warned that the heat is set to reduce their harvests this year.
The French government was expected to hold an inter-ministerial meeting on Wednesday to discuss the impact of the heatwave on the agricultural sector.
In Germany, temperatures were forecast to reach 39 degrees Celsius on Thursday in the southwest of the country and around the capital Berlin, possibly surpassing record levels reached in 2003, forecasters said.
In a move that would bring further misery for farmers, the German animal protection federation has called for animal transports to be stopped because of the heat, saying police had to rescue pigs who nearly died of thirst in a truck stuck in a traffic jam.
Also in Germany, navigation on the river Elbe in the north of the country was disrupted after water levels dropped below navigable levels.
The water was just 90 centimetres deep in parts, four months after the river flooding its banks. Commercial vessels which need water levels of at least 2.3 metres were diverted into canals which were not as badly affected.
In Britain, the heatwave that has already lasted 10 days in many parts of the country was expected to produce higher temperatures mid-week before finally ending at the weekend.
The national Met Office said London could see temperatures of 34 degrees Celsius on Wednesday, a few degrees short of the July record of 36.5 Celsius that was set last week.