Temperatures are forecast to hit 27C in Melbourne on Sunday and 25C in Canberra - their warmest September day in three years.
A 27C day is also forecast further south in Hobart, which would be the Tasmanian capital's highest September temperature since 2019.
"It is going to be warm," Bureau of Meteorology senior meteorologist Dean Narramore told AAP.
A high-pressure system in the Tasman Sea and a front crossing Western Australia are driving the warm weather, pushing northerly winds to the country's southeast.
Parts of WA recorded their warmest-ever September day on Friday, including Albany, where temperatures reached 31.8C.
Mr Narramore said the system would likely bring winds of 60 to 80km/h to Melbourne and 80 to 100km/h to Hobart on Sunday, with higher gusts likely on elevated terrain.
"Damaging wind warnings are likely to be issued this afternoon for Sunday ... and that is going to drive elevated fire dangers," he said.
For Tasmanians, that will repeat the strong gusts on Friday night that topped out at 141km/h on Kunanyi/Mt Wellington.
Fires are less likely in Victoria and South Australia than in parts of NSW and Tasmania given recent rainfall.
"It hasn't quite dried out (in Victoria and SA) enough, but it's been fairly dry in eastern Tasmania and eastern NSW so that's why hot, dry winds combined with the fuel load is leading to high fire dangers," Mr Narramore said.
Sunday's forecast temperatures don't come close to all-time September records in those centres, but will most likely be the warmest weather millions of Australians have experienced since last autumn.
The unseasonal warmth will be followed by a dose of typical spring shock therapy, with forecasts returning to the mid-teens on Monday and Tuesday before a rebound into the mid-20s later in the week.
"We're feeling it because these warm bursts are coming before really cold bursts," Mr Narramore said.Â
"We're feeling a kind of weather whiplash: the spring roller-coaster we get."
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