The heatwave, which will push the mercury to the high 40s in many inland areas across SA, Victoria and NSW, is expected to last until the weekend, with the danger peaking late in the week as hot, strong winds push ahead of a cooler change.
In Melbourne, which will endure a series of days in the high 40s, on-court temperatures at the Australian Tennis Open could reach as high as 50C.
Baking days and hot nights will increase the risk to health.
Monash University researchers, who have linked heatwaves in the east to tropical cyclones in the west, found that during the 2009 furnace the Adelaide morgue ran out of room and Ambulance Victoria was swamped with a record tally of emergency calls.
The Victorian Health Department estimated that 374 "excess deaths" occurred during the worst week of the heatwave.
Monash PhD candidate Tess Parker wrote on The Conversation website that although it was not possible to directly attribute deaths solely to the heatwave, there was a clear spike above the normal death rate.
In South Australia the State Emergency Service is co-ordinating efforts to reduce the risk from conditions authorities warn could kill, especially the very young, the aged, and people with chronic health problems.
Doctors, nurses and paramedics are on high alert.
The Red Cross is phoning people it knows to be at risk three times a day, and state, local government and private businesses are ensuring swimming pools and air-conditioned facilities are available.
In Victoria, where similar efforts have swung into action, public transport employees are providing water to commuters.
Health officials are advising people to keep drinking water even if they do not feel thirsty, to call for help immediately if suffering heat stress symptoms such as heavy sweating, headache, vomiting, confusion or swollen tongues, and to check on family and friends.
In Perth, easing conditions on Sunday night enabled fire crews yesterday to contain fires in the Perth Hills that forced thousands of people to flee to evacuation centres from Parkerville and nearby areas such as Mt Helena and Stoneville.
One man collapsed and died while preparing the roof of his house as fires approached, another was taken to hospital after falling through the roof of his home, and a 74-year-old man was evacuated from the fire zone after suffering chest pains.
Perth and much of southern WA cooled yesterday, and rain and lower temperatures are forecast during the week for northern regions - although the fire risk yesterday remained extreme or severe for the Goldfields, Gascoyne, Exmouth and Eucla.
As Adelaide sweltered in 40C heat - rising to as high as 43C in the next few days - health authorities issued a week-long extreme heat warning, and the fire danger climbed to severe across the state's mid-north, Mt Lofty Ranges, Yorke Peninsula and the lower southeast.
Melbourne will be scorched by temperatures of about 40C for much of the week, rising to the high 40s in many inland areas. High to severe fire risk extends across most of the state.
While Sydney and other coastal centres in NSW are likely to escape the worst of the heatwave, conditions elsewhere in the state will soar into the 40s. The fire danger has been rated as high to severe.
