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Sunscreen and icepacks were the order of the day on Thursday as temperatures hit 40 degrees Celsius in the late afternoon but 31-year-old Federer was coolness personified in the early evening as he dismissed Nikolay Davydenko 6-3 6-4 6-4.
Third seed Williams, also 31, kept her time on court to a minimum as she swept aside Garbine Muguruza 6-2 6-0 before Andy Murray, her counterpart in the men's draw, clinically despatched Portugal's Joao Sousa 6-2 6-2 6-4.
Not everybody got off so lightly, however, and Blaz Kavcic slugged it out for four hours and 52 minutes on court three against James Duckworth in ferocious heat in the middle of the day before winning 3-6 6-3 6-4 6-7 10-8.
"Total physical collapse after the match," the Slovenian Tweeted lightheartedly along with a picture of him receiving medical treatment in the locker room. "Feeling quite happy though, just don't know, because of my win or morphine."
Women's defending champion and world number one Victoria Azarenka, 23, proceeded easily enough in the relative cool of the morning with a 6-1 6-0 thrashing of Greek Eleni Daniilidou.
Any hopes the Belarussian had that Williams, against whom she has a 1-11 record, might be hampered by the ankle she injured on Tuesday were quickly dashed in the next match on Rod Laver Arena, however.
The American, odds-on favourite to de-throne Azarenka and capture a 16th grand slam title next week, gave herself a fat lip with her own racket during the first set but was barely troubled otherwise.
"I didn't feel anything today," Williams, who later played doubles, said of the ankle injury.
"Usually I feel injuries after the match, but so far, so good. I felt much better than I ever dreamed of expecting to feel. I'm on the up and up. It can only get better from here."
Federer, chasing an 18th major title here, will next face 20-year-old Bernard Tomic and the Swiss, who needed a fraction under two hours to beat Davydenko, was quick to warn the Australian that he was probably fitter than 10 years ago.
"I'm much more experienced today. I know what I can expect from myself in terms of my level of play early on," the second seed said.
"I'm much stronger today physically clearly so I can always rely on that as well, extend the rallies, so don't have to be worried about that."
Seventh seed Jo-Wilfried Tsonga overcame Japan's Go Soeda 6-3 7-6 6-3 and was joined in the third round by fellow Frenchman Richard Gasquet, who beat Colombian Alejandro Falla 6-3 6-2 6-2.
Gael Monfils also progressed but only after double-faulting on four successive match points before finally clinching a 7-6 4-6 0-6 6-1 8-6 victory over Lu Yen-Hsun of Taiwan.
"It was a bit crazy," the flamboyant Frenchman said. "It was like, 'I need to hit an ace because I know it's going to be a double-fault for sure'. It was weird."
Veteran Kimiko Date-Krumm, the women's world number 100, is fast becoming a cult hero at Melbourne Park and she continued her fairytale run with a 6-2 7-5 win over Israel's Shahar Peer.
"It's not easy, not easy," the 42-year-old Japanese said. "I need a new body."
Former world number one Caroline Wozniacki was also feeling her age after her encounter with Croatian Donna Vekic, which she won 6-1 6-4.
"I've been out here for a few years now and I feel like a veteran, particularly when I'm playing against a 16-year-old," she said.
"I'm seriously starting to feel old and I'm 22! I got asked a few months ago if I was going to retire."
The outer courts were again the place to go for upsets with the highlight being Ricardas Berankis's 6-2 6-3 6-1 hammering of 25th seed Florian Mayer on court six.
The Lithuanian will meet Murray next and the convincing nature of his win indicated he might prove more of a handful for the Scot than the limited Sousa.
The US Open champion used all the weapons in his armoury in the 101-minute contest and every one of them was superior to that possessed by his Portuguese opponent.
"You need to get in control of the points and dictate them because otherwise you will get very tired very quickly in these conditions," said the 25-year-old Murray.
His compatriot Laura Robson was one of 11 teenagers to reach the women's second round and she became the third to progress when she beat former Wimbledon champion Petra Kvitova 2-6 6-3 11-9 well past midnight, giving Britain two female players in the third round of a grand slam for the first time since 1991.