With an average temperature of 21.95C - 2.75C above than the long-term average - September 2013 also set a new high for the largest temperature anomaly for any month on record.
Climate experts say the records are consistent with the long-term warming trend linked to human-caused climate change.
The average temperature across Australia from October 2012 to September 2013 was 23.06C, or 1.25C above the long-term average of 21.81C (calculated between 1961 and 1990).
The new record bumps the September 2012 to August 2013 period to second place, when temperatures were 1.11C above the long-term average.
Australia is likely to break further records in the remaining months of the year, and could see 2013 become the hottest calendar year ever. The previous hottest year was in 2005.
Rewriting state and regional records
September saw state records fall too, with South Australia, Victoria, New South Wales, Queensland and the Northern Territory all recording the hottest September on record.
South Australia, the Northern Territory, and southern Australia also broke state 12-month records.
Sydney, Melbourne and Adelaide had their hottest September on record. At least 30 Queensland towns recorded their hottest September day in the last week of the month.
Central Australia saw a record-breaking string of high temperatures, with Alice Springs recording 20 days over 30C. The previous earliest period of high temperatures was late October.
The warm start to spring also saw an early start to the bushfire season in Sydney.
More extreme, more often
Professor David Karoly at the University of Melbourne has analysed the role climate change plays in weather extremes.
The new hottest 12-month record was at least 150 times more likely when simulations included human-caused climate change, he said.
“We’re experiencing hotter record temperatures averaged across the country, and this is indicative of the long-term warming trend.
"Our analysis shows that the major contribution to setting this new record has been the increase in greenhouse gases in the atmosphere in addition to natural variability.”
“The typical return period for these sorts of records has been dramatically reduced. It used to be 1-in-30 to 1-in-40 years; now, due to climate change, it is much more frequent.
"In the future these sorts of records will become even more common. They will become the norm 10 to 20 years into the future.”
Sarah Perkins, postdoctoral research fellow at the University of New Wales, said 2013 was unusual because current atmospheric conditions should have favoured average temperatures.
“These records are being set in a ‘neutral’ period of the El Niño-Southern Oscillation cycle (neither El Niño or La Niña), as well as a Negative Indian-Ocean Dipole pattern, which is normally associated with higher than average rainfall over southern and western Australia during the cooler months.”
She warned records could have been “much worse” if El Niño conditions had prevailed over summer.
The unseasonal heat bodes ill for the fire season, warned Professor David Bowman at the University of Tasmania.
“We’ve seen an early start to the fire season in New South Wales. It’s a warning shot, particularly for the southern areas.
"If you live in a flammable landscape, you’ve got to take this very seriously and think through strategies and planning.”
Warm conditions and rain have led to increased fuel loads, which would dry out over just a couple of hot days, Professor Bowman said.
He advised people to plan now to avoid disaster later, and urged people to consult state bushfire services.
“The worst thing people can do is not have a plan, or deviate from a well-thought through plan at the last minute. That’s when bad things are going to happen.”