MELBOURNE, Australia — Serena Williams   was having what she called an “out-of-body experience” Wednesday in brutal heat at the Australian Open.

Closing the Rod Laver Arena roof and cranking up the air conditioning helped the defending champion pull herself together and advance to the semifinals—but left her opponent steaming.

“I felt I was watching someone play in a blue dress, and it wasn’t me, because it was so hot out there,” said the second-ranked American, who beat Russia’s  Svetlana Kuznetsova  5-7, 7-5, 6-1. “And I kept trying to tell myself that it’s not hot. But it got hotter.”

Williams, seeking her fourth Australian title and 10th Grand Slam championship overall, next faces Olympic gold medalist  Elena Dementieva, who had to play her entire match with the roof open. The fourth-seeded Dementieva ousted  Carla Suarez Navarro  6-2, 6-2 to run her winning streak to 15 matches after she won two tuneup tournaments.

Top-ranked  Rafael Nadal  won his fifth match without dropping a set by beating Gilles Simon  6-2, 7-5, 7-5, though he was strongly tested by the sixth-seeded Frenchman. Simon broke his serve three times—matching Nadal’s total for the tournament—and had a set point with the Spaniard serving at 4-5 in the second set.

But Nadal was up to the task, ripping several winners on the run that were never inside the court until they landed and skipped away untouched.

Simon won their last meeting in Madrid in October.

“I was coming to the match with some doubts,” Nadal said. “But I knew I was playing better here.”

Simon is one of the quickest players around, but Nadal ground him down by constantly sending him sprinting from corner to corner. Even with the roof still closed, the lanky Simon was pouring out sweat.

Nadal got his seventh service break on a forehand that caught the line for a 6-5 edge in the third set, then held at love with Simon sending a forehand long on match point.

His victory set up an all-Spanish semifinal after 14th-seeded  Fernando Verdasco—the lowest-ranked player to reach the quarterfinals—beat No. 5  Jo-Wilfried Tsonga, last year’s runner-up, 7-6 (2), 3-6, 6-3, 6-2.

“I think it’s incredible for us,” Nadal said. “One will be in the finals, so we have to be happy with that.”

The heat wave is forecast to continue Thursday. If Williams wins— Dementieva has won their last three meetings, including the Olympic quarterfinals—she would play a Russian for the third consecutive match in the final. Third-seeded  Dinara Safina  is facing fellow Russian  Vera Zvonareva in the other semifinal.

“Me against the Russians, I guess,” Williams said.

With temperatures soaring to 109 degrees on a cloudless day—Williams had her rackets restrung during her match because they lost their tension—the retractable roof was closed after Kuznestova won the first set.

The heat was beginning to take a toll on Williams, and the eighth-seeded Kuznetsova was angry at the decision. She felt that the break gave Williams time to recover and that playing indoors benefited the American’s powerful serve.

“Why should I not be?” Kuznetsova said. “Game going my way. I was very comfortable playing outside. It’s two different games. One you play inside; one you play outside. Serena was tough. She’s playing great. I give her credit. But I don’t get this rule.”

Neither did other players.

Even though Dementieva won, she felt the roof should have been closed before her match started. Tournament officials called a news conference to explain the decision-making process, bringing in the official doctor and meterologist to talk about the “Wet Bulb Globe measure” that determines when it’s too hot.

“We do this to protect the players and to protect their ability to perform optimally,” said tournament director Craig Tiley.

The roof was closed for the first time during a match under the tournament’s evolving heat policy, which was changed after a heat wave two years ago. At that time, matches which started under open skies had to finish that way.

Down a set and a break and with Kuznetsova serving for the match in the second set, Williams broke to get even at 5-5 when Kuznetsova missed an open-court volley that turned the match.

Williams held and again broke Kuznetsova’s serve, forcing the deciding set. The American broke to lead 3-1 and, after saving two break points with a pair of forehand winners, the result was never in doubt.

Once again, Williams won despite playing far from her best—she had 18 unforced errors to four winners in the first set.

“My balls started flying,” she said. “They were pretty much hitting the people in the crowd. Definitely I was mortified at some of the shots I hit.”

The break helped her pull herself together.

“With the roof closed … it was definitely helpful,” she said.

Dementieva made a fast start against 20-year-old Suarez Navarro of Spain, who upset   Venus Williams  in the second round, winning 16 of the first 18 points for a 4-0 lead.

She raced through the first five games in 22 minutes and, after eventually holding serve in a sixth game that went to deuce 11 times and lasted 17 minutes, finished off in 1 hour, 35 minutes.