Most of Australia’s major cities are enduring an “extreme” end to 2016 with many being simultaneously inundated by rain and sweltering heat.

Melbourne, Brisbane and Adelaide will experience humid and wet weather this week, with the Northern Territory suffering the direst conditions.

At one stage on Tuesday, nine people were missing or in grave danger in NT following record rainfall and flooding.

Three Japanese tourists became trapped in their car after floodwaters washed it off a causeway near Alice Springs. Two of the tourists were quickly rescued, while the other remained trapped for hours before eventually being saved.

Meantime, six more people remain missing – thought to be stranded in central Australia – after attempting to drive from Kiwirrkurra, Western Australia, across the border to Kintore in the Northern Territory.

Similarly tropical weather hit metropolitan areas on Tuesday and was expected to continue through Wednesday and Thursday in Melbourne, Brisbane and Adelaide.

Storms, with possible lightning, could hit those cities over the next two days.

For Sydney, Bureau of Meteorology duty forecaster Kenneth Cheung told The New Daily the city would be exceptionally hot.

“Extreme heat wave conditions are expected for the north-east and mid-north coast of New South Wales,” Mr Cheung said.

“In central parts of New South Wales, severe conditions will be persisting over next few days. Then a change will come across on Sunday. Milder conditions will eventuate by the end of the week and into next week.”

From Wednesday to Saturday, Sydney is forecast to hit 30C, 37C, 33C and 31C. In the same period Canberra will hover between 31C and 32C and Melbourne will sit between 32C and 28C before dipping to 24C on Saturday.

From Wednesday to Friday, Brisbane is forecasted to experience temperatures of 30C, 31C, 32C and 35C. Adelaide will reach 32C on Wednesday, but will cool off for the rest of the week.

Authorities in Melbourne warned of a bushfire risk in the hot conditions on Wednesday and Thursday with winds expected to pick up significantly.

The forecast heat comes after spectacular scenes from Uluru on Monday.

The fury of Mother Nature shuts down Uluru-Kata Tjuta National Park in Central Australia. Being described as a once-in-a-half-century event. pic.twitter.com/eyJKSlJOxV

— Gautam Trivedi (@KaptanHindustan) December 26, 2016

Yulara, the tourist village at Uluru, broke its December rain record, previously set in 1987, as well as its 24-hour rainfall record, with 84mm falling in one day.

The downpour caused waterfalls to run down the sacred Aboriginal landmark.

No sign of missing family

The group missing in central Australia set off from WA in two cars on Christmas Day and included five adults and a baby.

It is believed they became bogged and search efforts have been hampered due to flooded roads and rescue cars also becoming stuck in the mud.

Emergency services gather to rescue the Japanese tourists. Photo: ABC

“Basically there’s been about 100km of that road we’ve been unable to search,” NT Police’s Acting Superintendent Brendan Muldoon said.

“The infant is with its parents. We don’t know what food or water they have with them, but there’s plenty of water in that area due to the flooding.

“We are concerned, obviously, and we’re making efforts to ensure we can locate them as soon as possible.”

Conditions have eased and an aerial search began on Tuesday afternoon.

Up to 30 people are still stranded at Glen Helen – west of Alice Springs – due to the flooding Finke River.

– with ABC and reporting by Luke Henriques-Gomes