Australian Associated Press reported that the aircraft, a 1994 Kawasaki BK117, had crashed into a tree.
Australia endured one of its hottest years on record in 2017, the nation's chief weather service said, while it was the hottest in more than a century for the country's most populous state, New South Wales.
The tragedy occurred at the Banksia Road Public School when the car smashed into a wooden classroom building not long after lessons started.
A homeless tent city in the heart of Sydney was being dismantled Friday, after political wrangling over the plight of those sleeping rough in winter sparked criticism and new laws.
Eastern Australia was bracing for severe "off the scale" fire conditions on Sunday as it baked in a heatwave that has broken temperature records and sparked dire warnings from authorities.