Pete Sampras said he was "on fire" during his five-set slog to victory over the Slovak Dominik Hrbaty, but on this occasion it was not his talent that was making sparks fly.
The No 1 seed fears that officials will take action only once someone has become seriously ill. "I think there's going to have to come a point where someone really gets hurt out there to make some sort of rule change," Sampras said after almost losing to the 19-year-old Hrbaty, ranked 76th in the world, in a match lasting nearly three hours.
The unwanted distinction of becoming the player to force that rule change nearly fell to an 18-year-old Briton, James Trotman, whose heart started to "go berserk" during his win in the first round of the boys' event. "I felt terrible after the first set," Trotman said. "The trainer tested my heart beat and it was going berserk."
Like desert explorers the players found that the greatest risks came if they gave up and sank to the ground.
Goran Ivanisevic fell to his knees after beating Norway's Christian Ruud in another three-hour battle and then realised it was not a good idea. "That was a mistake. I was almost burned, but I was so tired I had to fall down," he said.
"You cannot try the whole game, otherwise you die; after 10 minutes you're dead. I didn't feel too much in my legs. I was out of it, I didn't know where I was."
On Sunday, the Belgian 16th seed, Sabine Appelmans, had to be placed on an intravenous drip, while a defeated Steffi Graf was treated for heat exhaustion.
Gerald Segal, of the Australian Medical Association, said: "It could be just a matter of time before someone dies out there."
Under the rules of women's tennis, play can be delayed in extreme conditions. But an appeal by players to postpone their matches yesterday was overruled by the committee which runs the Grand Slam tournaments, saying it was unfair on those who had played the previous day.
The match between the Romanian eighth seed, Irina Spirlea, and the ninth seed, Karina Habsudova of Slovakia, was delayed by 30 minutes while officials reviewed their request.
"We were just asking if it's possible to play tomorrow," Spirlea said after winning 6-4, 6-4.
In men's tennis there are no rules governing extreme heat. Cooling fans were placed beside the courts yesterday and players draped ice-packed towels over their shoulders at the change of ends in an attempt to cool down.
"It was so hot today, it was a joke," Sampras said after eventually winning 6-7, 6-3, 6-4, 3-6, 6-4. "My feet were on fire and we were both feeling it."
On his victory, Sampras said: "There's an old saying, it's better to be lucky than good, and I definitely had a lot more luck than good today."
The fifth seed, Thomas Muster, overcame a series of injuries and a brief floodlight failure to beat the 11th seed, Jim Courier, in a match which lasted two hours 42 minutes and which ended in the early hours of Tuesday. Muster received treatment for shoulder and hip soreness and blisters on the feet during his 6-2, 3-6, 7-6, 6-3, victory.
Age provided some protection against the heat and certainly did not stop 16-year-old Martina Hingis in her drive to become the youngest Grand Slam champion. She survived a first-set scare to beat Romania's Ruxandra Dragomir 7-6, 6-1.
"I just wanted to win this game and I was just so nervous, I don't know why," Hingis said. "I just felt so different because it is a big Grand Slam tournament and there is a little chance - well, there is a big chance - to win."