Adelaide has been declared the hottest city in the world on Thursday by the United Nations' World Meteorological Organisation.

The city is on course for its hottest day ever recorded, as South Australia and Victoria swelters through another day over 40C.

It is set to reach 46C by 4.30pm on Thursday, Adelaide's fourth consecutive day above 40C. The temperature could pip the 46.1C record set in the city in 1939.

It was another uncomfortable night for Adelaide residents on Tuesday, with the temperature hitting 35.5C at midnight. The city’s central bus station, which is air conditioned, has been opened 24 hours a day for people to sleep in.

Large fans with water mist sprayers have also been set up at the Rundle Mall. The council said it is advising people to drink plenty of water, dress in cotton lightweight fabrics, avoid going out in the heat and use air conditioning and fans if possible.

Port Augusta is set to reach 47C, with nowhere in South Australia due to be cooler than 37C.

Adelaide is set to endure five consecutive days over 40C, while Melbourne is on course to have four days above this temperature, the first time this has happened since 1908. The Victorian capital is forecast to reach 44C on Thursday.

The heatwave, which has sat over south-eastern Australia since the start of the week, is showing signs of shifting further into New South Wales. The Bureau of Meteorology has forecast 43C for Wagga Wagga on Thursday and Friday, dipping slightly to 42C on Saturday.

A total fire ban is in place across South Australia and Victoria, with overnight lightning triggering dozens of fires. Victoria’s Country Fire Authority said Thursday would prove a “difficult day” for firefighters, warning that conditions on Friday, when wind strength is set to increase, will be “critical”.

More than 70 people have been hospitalised in South Australia this week due to the heat. In Victoria, the ambulance service has warned people not to leave children locked inside cars, having attended to 11 such cases, including an incident where a child was apparently deliberately left in a car outside a bottle shop.

The Australian Energy Market Operator (AEMO), which oversees energy demand, said Victoria and South Australia have increased power usage to levels not seen since 2009.

The Victorian government said up to 100,000 homes and businesses could suffer power blackouts due to the surge in demand in the coming days.

AEMO said some areas may experience “localised interruptions over the coming days as a result of the extremely hot conditions, and forecast high winds and lightning in some parts of Victoria and South Australia”.

The hot weather also has grape growers in South Australia’s wine regions fretting. They fear the heat could destroy up to 20% of their crop.

And in Melbourne, three Australian Shakespeare Company outdoor performances were cancelled on Tuesday evening due to high temperatures. The company said it didn’t expect planned performances of the Wind in the Willows and Alice in Wonderland to be disrupted again.

Tony Leggett, senior meteorologist at the Bureau of Meteorology, told Guardian Australia the current heatwave is slightly different from the high temperatures in 2009 that led to the deadly Black Saturday fires in Victoria.

“We’ve been looking at the synoptics and there are a few differences that suggest we could have fewer fire problems this time, although of course there are lots of other variables in there other than just the weather,” he said.

“In 2009, we’d had a decade of dry conditions and the bushland had dried out. We are only just seeing the bush start to dry out this time, but if we got another heatwave in February, we’d expect the fire danger to increase with that.

“It’s difficult to say that this heatwave is induced by anthropogenic warming, the atmosphere is a bit too chaotic for that, but if you look at the trend in overall temperature, it’s logical to say we’ll be having more extreme bursts of temperatures in the future. The trend line is ever upwards.”