In Victoria, lightning strikes sparked more than 250 fires on Tuesday night, fire authorities said. A fire ban has been issued across the state.
In Melbourne, a tennis player and a ball boy at the Australian Open collapsed in the heat.
Temperatures in the city remained above 30C for much of Tuesday night.
Country Fire Authority chief officer Euan Ferguson said in a statement: "The extreme temperatures [in Victoria] over the coming three days will test fire services and the community. It's critical we minimise the risk of any fires before Friday."
Firefighters have been able to contain most of the fires in the state, although a number of fires remain out of control.
Emergency fire warnings have been issued for the Victoria communities of Yaapeet and Nypo, with fire authorities urging residents to evacuate due to "a fast moving, out of control bushfire travelling in a south easterly direction".
In 2009, fires in Victoria killed 173 people and destroyed 2,000 homes.
Meanwhile Adelaide, the capital of South Australia, experienced its fourth hottest day on record, reaching 45.1C (107F).
More than 14,000 properties have experienced power cuts, with many thought to be caused by thunderstorms and lightning strikes, ABC reported.
In Tasmania, there were reports of road tar melting in the heat.
Croatian tennis players Ivan Dodig feared he "could maybe even die" before retiring from his match as heat was once again a significant factor on day three of the Australian Open.
After temperatures of 42C (107.6F) on Tuesday, there was a peak of 41.5C, with greater cloud cover, on Wednesday.
Dodig, 29, withdrew two hours and 22 minutes into his second-round match with Damir Dzumhur in Melbourne.
"Thirty minutes after the match, I could not walk," he said.
Bush fires in Western Australia destroyed more than 50 homes earlier this week, the BBC's Jon Donnison in Sydney reports.
Last year was recently declared Australia's hottest on record, further raising questions about the impact of climate change, our correspondent adds.
South-east Australia has been hit with extreme hot weather, with temperatures of over 40C (104F) in some areas, and several bushfire warnings in place.