Conditions will remain unseasonally humid until late Monday, Bureau of Meteorology forecaster Dean Stewart says.
"It's unusual that you'll have high temperatures combined with the very high humidity," he told AAP on Saturday night.
"It doesn't often get this humid when you've got temperatures around 40C."
Humidity interferes with the body's ability to cool itself and intensifies the effects of heat stress.
People have been urged to drink plenty of water, stay inside and look out for vulnerable family and friends, particularly the very young and elderly.
"The weekend is getting hotter and the heat will extend into Monday for all Victoria," Emergency Management Commissioner Craig Lapsley tweeted on Saturday afternoon.
"Look after each other, overnight temperatures are very high for Saturday and Sunday nights." People will get a reprieve from the hot and sticky conditions with a cool change expected to hit Melbourne on mid-Monday afternoon, BoM says.
Total fire bans have been declared for parts of South Australia as extreme heat continues to blast the state.
Adelaide is forecast to reach 42C on Sunday, Whyalla and Murray Bridge 44C and Port Augusta, Marree and Roxby Downs 46C.
Total fire bans have been declared for the Adelaide metropolitan, mid north and Mt Lofty Ranges areas.
It's Adelaide's second heatwave this month, following similar conditions the week before which led to the hospitalisation of 40 people.
A cool change is set to bring to bring relief later on Sunday ahead of a forecast top of 29C in Adelaide on Monday.
Elsewhere across the state, conditions are expected to reach into the mid-30s but the north of SA will remain very hot.
Meanwhile, the Northern Territory is being battered with heavy rain and strong winds.
People in the southwest region of the Top End have been warned to stay alert as a tropical monsoon low moves in, bringing heavy rain, with as much as 50mm to 100mm expected in a 24-hour period.
The low is also bringing damaging winds with gusts up to 90km/h and the risk of flash floods.
Residents in Daly, Gregory and parts of Carpentaria, Barkly and Tanami districts have been warned to be vigilant.
Other places at risk include Darwin, Wadeye, Nauiyu, Palumpa, Lajamanu, Kalkarindji, Timber Creek and Top Springs.
Early on Saturday morning, wind gusts of up to 74km/h had been recorded at Darwin.
Victoria's chief health officer Professor Charles Guest warned the current heatwave in the state could be fatal.
According to Fairfax media, Professor Guest said elderly Australians were more at risk as they were less likely to use airconditioning.
"We know every time there is a succession of hot days there will be deaths," he said on Friday morning.
"Think of your neighbours and friends. Particularly old people living alone are vulnerable to the heat and not aware they are becoming victim to heat exhaustion."
Beachgoers have also been warned to swim between the flags and avoid rips following a recent spike in drowning deaths across the country.
ADELAIDE:
The South Australian capital will be mostly sunny and very hot with a high of 41 degrees today, before climbing even higher to 42 degrees tomorrow.
There will be a cool change on Monday though with the mercury plummeting to 26 degrees.
MELBOURNE:
Melburnians will face humid conditions with a possible shower today with a high of 32 degrees, followed by a scorching hot, humid and mostly sunny 39 degree day tomorrow.
HOBART:
The city will be very hot, humid and sunny at 36 degrees today, with a high of 30 degrees tomorrow and a chance of showers.
SYDNEY:
It will be partly cloudy and a reasonable 28 degrees in Sydney today and tomorrow.
BRISBANE:
There will be a shower or two in Brisbane today with a high of 30C, followed by more showers and a high of 30 tomorrow.
PERTH:
It's expected to be mostly sunny and 29 degrees today in Perth, with clouds clearing and a high of 30C tomorrow.
CANBERRA:
There will be a shower or two and a possible storm with a high of 31 in the nation's capital today, with a partly cloudy 33 degrees tomorrow.
DARWIN:
Possible storms and a high of 29 are predicted in Darwin both today and tomorrow.
