SYDNEY—A string of wildfires burned across Australia's south and east following a record run of sweltering heat, while residents girded for a major heat wave Tuesday that threatened to make things worse.

Temperatures in New South Wales—the country's most populous state—were forecast to reach 43 degrees Celsius (around 109 degrees Fahrenheit) and stay high over the coming days. More than 90 fires are already burning across the state.

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