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Victoria and South Australia are tipped to endure the worst of the conditions, but NSW and Tasmania will also feel the hot air mass spreading from the west.
Adelaide continues its five consecutive days of temperatures above 40 degrees, with 42C forecast for Tuesday, 43C on Wednesday and Thursday and 40C on Friday before a cool change.
Melbourne is forecast to top 40C on Tuesday, Thursday and Friday, with 39C predicted for Wednesday.
Victorian Fire Service Commissioner Craig Lapsley says the heatwave will bake Victoria's bush and grassland, creating perfect bushfire conditions.
Ambulance Victoria manager of emergency management Paul Holman described this week's conditions as the worst heatwave since the lead-up to the 2009 Black Saturday fires.
During Victoria's 2009 heatwave 370 people died from heat-related illnesses and there was a 46 per cent increase in calls to triple zero in three days.
South Australian Premier Jay Weatherill has urged all people to take care of those most vulnerable to the heat, including elderly relatives, friends and neighbours.
He says people without air-conditioning at home should consider heading to cooler public facilities such as cinemas, shopping centres and libraries.
Sydney will be spared the worst of the weather, with temperatures in the high 20s in the city and high 30s in the city's west.
A total fire ban has been declared for southern Tasmania on Tuesday and parts of the state's south will reach the mid to high 30s during the next few days.
After a weekend of extreme heat that triggered bushfires, Perth will experience a mild week before temperatures hit the high 30s at the weekend.