The heat wave pushed temperatures up to 46 degrees Celsius (115 Fahrenheit) in some parts of Greece, killing two people, the Health Ministry said.
The ministry said two pensioners, aged 84 and 76, died Monday in Aegio, in southern Greece, and in the central city of Larissa.
Temperatures are expected to remain high for a second week, reaching 43 degrees Celsius (109 Fahrenheit) in Athens.
Hospitals and municipal facilities are on alert around the country, while other state-run public services will close early, at noon, on Tuesday and Wednesday.
National electricity consumption exceeded 10,000 megawatts Monday, fueled by heavy air conditioning use, causing limited power outages in greater Athens, the northern city of Thessaloniki and several Greek islands.
The government urged the public to avoid unnecessary energy consumption but insisted the national grid had been adequately strengthened to avoid widespread outages.
"The system had been reinforced to withstand even higher levels of consumption," Nikos Stefanou, general secretary of the Development Ministry, told private Antenna television. "Of course there will be damage to parts of the network to overheated cables and similar problems."