An oppressive heatwave stretching across half the country from Darwin to Victoria will send temperatures soaring up to 15 degrees Celsius above average during the coming days.

Maximums are predicted to exceed 40C across a broad swathe of the interior and east — the warmest summer weather in years for much of south-east Australia, including highs on Monday of 41C in Melbourne and 38C in Canberra.

Across the eastern outback maximums will peak well above 45C, hot enough to challenge December records in a handful of western New South Wales towns.