Melbourne is expected to bake on Monday, with the Bureau of Meteorology forecasting a top of 37C after a low of 24C.
Hot weather is predicted across most of Victoria, with temperatures in the mid to high 30s likely.
An extreme fire danger rating is in place for the South West region of Victoria, with emergency crews on high alert.
Adelaide is also sweltering, with the state's capital tipped to peak at 38C after an uncomfortable overnight minimum of 27C.
Hot conditions in the high 30s and low 40s are forecast for most regional areas in South Australia, with a total fire ban widely declared.
The bureau warns the conditions will persist in parts of SA, Victoria, NSW and Tasmania until Wednesday.
The temperature in Melbourne is forecast to reach 37C on Monday. (Joel Carrett/AAP PHOTOS)
The temperature peaked at 36.9C in Melbourne late on Sunday, with Avalon recording 40C and Geelong 39.6C.
It followed a record-breaking Saturday night in the Victorian capital, with the mercury hovering about 30C until Sunday morning, when it dropped to 27.3C - toppling the previous March record-high minimum temperature of 26.5C in 2013.
Hobart was also stifling on Saturday night, with a minimum temperature of 24C, well above the previous March record of 21.1C.
In SA, Adelaide recorded a top of 38.8C on Sunday as the mercury soared into the high 30s and 40s across most of the state.
The warmer weather, roughly 10 to 15 degrees higher than average is caused by a high-pressure system sitting in the Tasman Sea that directs hot northerly winds over south-eastern Australia.
The Bureau of Meteorology says those "blocking high-pressure systems" also prevent cold fronts being able to sweep across the southern parts of the country and flush away the heat.
"A southerly change is expected to move through early on Tuesday, giving the southern states some reprieve but it won't be until Wednesday or Thursday that a colder air mass will push in and bring those temperatures down," senior meteorologist Sarah Scully told ABC News.
Extreme conditions on Saturday forced event organisers to cancel some outdoor festivals and parades.
Melbourne's famous Moomba Parade was cancelled on Saturday due safety concerns for performers and spectators.
Patrons at the Pitch Music and Arts Festival in southwest Victoria were told to leave by Saturday morning as those yet to arrive were warned to stay away.
One of the stages at Adelaide's WOMAD was closed on Sunday due to the heat, while a handful of other events were postponed until late at night or cancelled.
20°C