Weather forecasters say a large mass of hot air is travelling across the Mediterranean from North Africa.
Southern Europe is experiencing scorching heat as temperatures reach more than 40 degrees Celsius in many countries.
The authorities in several cities have been forced to take measures to look after elderly people in particular.
Severe heat warnings in Italy
The Italian health ministry placed 14 cities under the most severe heat warning earlier this week, including in Rome, where it reached 41 degrees on Friday. This could well extend to around 17 other cities in the coming days.
Four people have already died from the heat.
In the capital tourists and residents have been cooling off in the city's fountains.
Heat awareness campaign in Spain
Spain is sweating under its first official heatwave of the year with temperatures in Madrid rising to the high thirties.
The Spanish government has launched a heat risk awareness campaign for people working mostly outside.
The "with sun it's time for caution" campaign warns of heat-related risks such as heat stroke and solar radiation.
Spain's State Meteorological Agency has also issued an orange-level severe heat alert in some parts of the country.
This could see the banning of some outdoor working under a government decree introduced last year which was put in place to help the country cope with more frequent heatwaves.
Outdoor work bans in Greece
In Greece outdoor work such as manual labour, deliveries and construction, has already been banned during the hottest time of day.
The Acropolis in Athens was also closed for several hours in the middle of the day earlier this week.
Night-time temperatures in parts of Athens have remained above 30 degrees for the past 10 days.
Rural fire risks in Portugal
The Portuguese Sea and Atmosphere Institute has warned there are around 40 municipalities at high risk of rural fires due to the ongoing hot weather.
The highest maximum temperature forecast of 40 degrees Celsius is expected to be reached on Friday in the city of Évora and Beja, with 40ºC.
In Lisbon, the maximum temperature this Friday is expected to be no more than 31ºC, but forecasts point to a rise in temperatures from Monday onwards, with thermometers reaching 36ºC.