Australian authorities have issued heatwave warnings for most of the country as millions celebrate Australia Day.

Temperatures are expected to peak on Tuesday, reaching the high forties Celsius in the southern states of Victoria and South Australia, the Bureau of Meteorology said.

On Sunday, South Australia recorded temperatures as high as 48.5C, according to the bureau, which is warning of fire danger in parts of the country.

Some national day celebrations on Monday have been cancelled out of safety concerns.

Australia Day - 26 January - marks the anniversary of the 1788 landing of Britain's First Fleet, which began the era of colonisation. In Adelaide, an Australia Day parade and light show have been cancelled due to the extreme heat forecast.

While this is deeply disappointing for the community, performers and partners, community safety and wellbeing must come first, organisers said.

Apart from Victoria and South Australia, heatwave warnings have also been issued in New South Wales, Queensland, Tasmania, Northern Territory and the Australian Capital Territory, with many remaining until Wednesday.

We haven't seen heatwave conditions like this in Victoria for almost 20 years, warns Tim Wiebusch, Victoria's emergency management commissioner.

On Monday, the Bureau of Meteorology warned of extreme fire dangers across parts of South Australia and much of south-western Victoria due to very hot and dry weather coupled with gusty winds.

Firefighters in Victoria are battling several fires, prompting evacuations and threatening properties.

The heat has affected the Australian Open at Melbourne Park. Player Jannik Sinner was seen suffering from cramps on the court, and nearly 80,000 fans were asked to take care in the blazing sun.

Meanwhile, Tropical Cyclone Luana battered parts of Western Australia, causing damage before weakening as it moved inland.

Authorities recommend finding cool spaces like homes, libraries, or shopping centres, and advise closing windows and drawing curtains to keep homes cool.