World number one Serena Williams wasted little energy in winning her Australian Open second-round match 6-1 6-2 against Serbia's Vesna Dolonc.
Temperatures again hit 40C, and Williams said: "It was tough conditions out there. I think it keeps getting hotter.
"I'm just drinking a lot, making sure I stay hydrated. I kept waking up in the middle of the night last night paranoid. I just wanted to stay hydrated.
"The last thing I want to do is to cramp in this weather. It can happen so easily."
Next up the top seed meets 31st seed Daniela Hantuchova, who needed more than three hours to see off Karolina Pliskova 6-3 3-6 12-10.
Wimbledon finalist Sabine Lisicki said she had been beaten by the heat after a surprise loss to Monica Niculescu of Romania while home hope Casey Dellacqua upset 18th seed Kirsten Flipkens 6-3 6-0.
Fourth seed Li Na was first up on Rod Laver Arena on Wednesday against 16-year-old Swiss Belinda Bencic, having knocked out another 16-year-old, Croatian Ana Konjuh, in the first round.
Li had little trouble against Konjuh and it appeared it would be the same again but Bencic gave notice of just what a talent she is by fighting all the way before going down 6-0 7-6 (7/5).
Bencic is coached by Melanie Molitor, the mother and former coach of Martina Hingis, and Li said: "She played exactly like Martina Hingis.
"She gave me a very tough time at the end of the second set. But I was really happy in the end I could use my experience to win the match.
"If she plays more tournaments on the tour, for sure she would be very good."