Temperatures in London, Paris, Berlin and Frankfurt could be as much as 10°C above average this week. In Spain, the weather agency, said 42°C could be recorded in the south.
Large swathes of western Europe will experience the first warm spell of the summer season this week with temperatures expected to climb by up to 10 degrees above the seasonal average.
According to Accuweather, "high temperatures from London to Paris, Frankfurt and Berlin will average 5-10 degrees C above normal by the middle of the week."
"While much of Germany had hot weather on the 12th and 13th of June, the coming warmth could rival some of the warmest conditions yet this year across Wales, England, France and Low Countries. This is quite a stark change from the recent cooler and, at times, wet weather," it added.
The French meteorological agency, Meteo France, said the country's "first heat peak" of the season should start on Monday with particularly warm temperatures expected on Wednesday, Thursday and Friday.
"We will often reach 32 to 34°C", it said in a statement, adding that "the threshold for very hot weather (35°C) could be exceeded locally".
AEMET, the Spanish weather agency, explained that "a very warm mass of air" coming from Africa combined with "stable atmospheric conditions" will push temperatures up across most of the peninsula and the Balearic islands.
In Mallorca, temperatures could reach 34°C but it should be even hotter on the mainland.
Temperatures along the Ebro valley, in the north-east, could reach 35 ºC; in the Tagus valley, in central Spain, they could climb to 38 ºC; while in the Guadalquivir valley, in the southern region of Andalusia, they could be as high as 40-42 ºC.
"This episode of high temperatures is expected to last until Thursday, when a decline is likely to start that will soften temperatures at least until Sunday, the 28th," AEMET said in a statement.
2019 was the warmest year on record for the Old Continent with three periods of exceptionally warm weather observed in February, June and July, according to the European Centre for Medium-Range Weather Forecasts (ECMWF).
The summer heatwaves led to record-breaking high temperatures.
In Europe, 11 of the past 12 warmest years have occurred since 2000.
"Globally, climate indicators show that the most recent five-year mean is 1.1ºC above pre-industrial levels, and across Europe it is almost 2.0ºC above the level seen in the second half of the 19th century," ECMWF said.
According to the European Environment Agency, extreme heatwaves as strong or even stronger than the ones observed in Europe since the turn of the millennia, "are projected to occur as often as every two years in the second half of the 21st century."