Organisers suspended play on all outside courts at Melbourne Park just before 1.30pm on Tuesday after determining conditions had reached level five on the Open's heat stress scale.
The rooves of Rod Laver and Margaret Court arenas were closed so the men's singles could continue.
Melbourne could come close to its hottest day on record of 46.4C in 2009, with a forecast maximum of 45C.
Usually-busy Garden Square and nearby eateries were almost deserted as the temperature in the precinct hit 40C at 2.30pm.
The Heat Stress Scale (HSS) was first implemented in 2019 amid concerns over player and spectator safety.
Four climate factors - air temperature, radiant heat, humidity and wind speed - are measured from various locations at Melbourne Park to determine the HSS measure.
An 11.30am start on Rod Laver Arena allowed women's world No.1 Aryna Sabalenka and Iva Jovic's quarter-final to take place with the roof open.
With the heat index passing four in the second set, players would have been allowed a 10-minute cooling break between sets.
But it wasn't needed as Sabalenka swept aside the wilting American 6-0 6-3 in less than 90 minutes.
The roof was closed about 1.15pm during the four-time major champion's on-court interview.
Sabalenka was grateful it was not fully open throughout the encounter so she could seek refuge in the shade between points.
"I knew going into this match that they won't let us play on crazy heat," she told reporters.
German third seed Alexander Zverev's quarter-final clash with American Learner Tien was played entirely under the roof.
Women's seeds Coco Gauff and Elina Svitolina open the night session from 7pm, before home hope Alex de Minaur takes on career slam-hunting Carlos Alcaraz.
A cool change was not expected to arrive in Melbourne until late on Tuesday evening, with the mercury tipped to still be 41C at 8pm.
The forecast raises the potential for both night-session matches to be held indoors.
De Minaur, the sixth seed, wasn't bothered by the forecast temperatures for his blockbuster clash with the Spanish world No.1.
"I mean, I'm Aussie. I don't mind the heat," the 26-year-old said.
"I have said it since day one. That's just what I have grown up with, and I'm ready for these types of conditions."
Alcaraz, meanwhile, conceded "you've got to get used to everything" as he puts the forecast heat out of his mind in preparation for de Minaur.
"Whatever it is, I just will be ready," Alcaraz said.
Svitolina, who is reached the quarter-finals for the second straight year, was hopeful her evening timeslot would grant some relief from the heat.
Officials on Monday confirmed a series of measures to combat the heat, including allowing ground pass ticket holders access to Margaret Court Arena.
Ballkids have reduced rotations, increased recovery times, and additional relief squads, while the start of the wheelchair championships was postponed to Wednesday.
34°C