Healthcare centres and critical sites were being prioritised in the effort, with generators provided to tide over retirement homes after Tuesday's outages blamed on a transformer incident, they said.
"The incident was accidental and related to the current heatwave," officials said in a statement on Wednesday.
"No one was injured."
Record-breaking temperatures across Europe, ranging as high as 18C above normal, according to the Reuters Climate Monitor, have disrupted transport networks and forced schools and tourist sites to shut.
Weather agency Meteo France has said the conditions were comparable to a heatwave in August 2003 that lasted 16 days and caused an estimated 80,000 excess deaths across Europe.
It was not certain how long the heatwave, driven by a weather pattern known as an Omega block, for a shape that allows temperatures to build day after day, would last.
Europe is warming at more than twice the global average, the World Meteorological Organisation has said, which makes prolonged heat episodes increasingly likely.
The heatwave has forced builders to alter working hours so that employees can avoid the worst, as retailers struggle to meet demand for fans and portable air-conditioners and farmers harvest grain at night after a ban on afternoon work due to fire risks.
Dozens have drowned as they sought to escape the heat by jumping into bodies of water.
In Britain, the grid operator asked generators to make more power available amid soaring temperatures poised to break records later on Wednesday.
With temperatures in the high thirties, British health authorities have issued a "red heat" health alert, for only the second time ever, warning of a risk to life for even the healthy, as well as the ill and elderly.
Britain's train operators have advised only essential journeys over the two hottest days of Wednesday and Thursday, as the heat has brought speed restrictions.
In southeastern France, two children aged two and four who died in a hot car outside their family home were shown on autopsy to have succumbed to the excessive heat.
Their mother said the children were in the car without her knowledge, the regional prosecutor said.
Italy's health ministry issued its highest heat alert for 16 cities, from Florence and Milan to Rome, Turin and Verona.
Conditions were expected to worsen further, especially across central and northern regions, with the heatwave likely to peak between Sunday and Monday, meteorologists said.
Temperatures could reach 41C between Tuscany and Emilia, while in coastal areas such as Liguria the combination of heat and extreme humidity could drive perceived temperatures as high as 45C.
