"It's my 30th birthday and it's awesome how the time is going".
And Barty was not the only crowd fancy to get her marching orders, with five-time Grand Slam victor Maria Sharapova roundly beaten by a surgically precise Angelique Kerber.
The win was a relief for Djokovic, who says he's still not 100 percent after six months off the tour with an injured right elbow and who lost in a second-round shocker here a year ago.
Kerber took the first set in just 29 minutes, displaying her trademark athleticism and forcing Sharapova into a number of erratic shots.
"It was obvious we both suffered on the court today", Djokovic said.
"I had a really tough off-season and I was working hard to be here and playing against the best players".
It's supposed to be even hotter on Friday, with a forecast high of 42 Celsius (108 Fahrenheit).
Sharapova, back in Melbourne after testing positive for a banned substance here in 2016 resulting in a 15-month ban, had looked menacing in the opening two rounds.
"I'm nearly dead", the tenacious Romanian said after the incredible battle, in which Davis lost a toenail and Halep served for the match four times.
Radwanska will now lock horns with Chinese Taipei's Hsieh Su-Wei in her next clash of the Australian Open.
The pair of of former world No.1s will meet in the round of 32 on Saturday, with reigning French Open champ Jelena Ostapenko the only other woman still alive in the women's draw to have won a grand slam crown.
Muguruza acknowledged that the heat was bothersome, but it wasn't the hottest conditions she'd experienced in Australia.
"I think there are a lot of things that I need to get better at and improve on", she said.
Kyrgios is now the only Australian with a chance to take an Open singles title.
He has been hailed as the leader of the tennis new guard but has now failed to go beyond the fourth round in 11 Grand Slams, admitting he has "some figuring out to do".
Pera will next play No. 20 Barbora Strycova.
"Everybody who knows me, they know that I never give up and I am always coming back".
Sixth seed Karolina Pliskova remained on course for a semifinal clash with Halep as she beat fellow Czech Fed Cup teammate Lucie Safarova 7-6 (7-6), 7-5 to move into the fourth round.