With the temperature exceeding 95 degrees, top-seeded Serena beat Hungary's Timea Babos 6-4, 6-1 and 16th-seeded Venus beat Kazakhstan's Yulia Putintseva 7-6 (7-5), 6-4.
With two more wins, five-time Wimbledon champ Venus would meet Serena, who is riding a 23-match Grand Slam winning streak and also seeking her sixth Wimbledon victory.
"She poses a big threat for me," Serena said.
Venus last won the tournament in 2008, and she has been playing through Sjogren's syndrome -- an autoimmune disease that can cause joint pain -- for most of this decade.
"I always root for Venus," Serena said. "She's been through a lot in her career. She's really playing well."
There were two upsets on the women's side, with 158th-ranked qualifier Bethanie Mattek-Sands knocking out No. 7 seed Ana Ivanovic 6-3, 6-4 and 47th-ranked CoCo Vandeweghe beating No. 11 Karolina Pliskova 7-6 (7-5), 6-4.
The day was slightly hotter than the 1976 record of 94 degrees.
"It wasn't as bad as I thought," Djokovic said. "People were talking about it and predicting really difficult conditions. But I didn't find it as difficult as I thought it might be."