Hewitt bore the brunt of the brutal conditions in a stunning 5-7 6-4 6-3 win over second seed Kei Nishikori of Japan.
And ex-world No.1 Federer was made to sweat it out by hard-hitting eighth-seeded Frenchman Jeremy Chardy before prevailing 6-3 6-7 (3-7) 6-3 in their semi-final.
Federer played in slightly cooler temperatures but Chardy turned up the heat on centre court, bouncing back from a lacklustre first set to take the second 7-3 in a tiebreak.
In contrast, Hewitt and Nishikori spent breaks between points with ice packs draped around their necks and on the back of their heads while nestled next to court-side fans as temperatures hovered around 40 degrees.
World No.60 Hewitt hung on to book yet another showdown with his long time rival and good friend.
Federer - a 17-time grand slam champion - holds an 18-8 record against Hewitt spanning 15 years, winning 16 of their last 17 encounters.
However, Hewitt won their last meeting on the tour, ending a string of 15 straight losses by prevailing in the 2010 Halle final in Germany.
Two-time grand slam champion Hewitt is enjoying the best start to a summer since 2005 when he made the Australian Open final against Marat Safin after overcoming world No.17 Nishikori.
Hewitt, 32, was up 40-0 serving at 5-all but was still broken before Nishikori sealed the first set with a stunning backhand winner.
Rather than drop his head and succumb to the heat, Hewitt again showed his fighting spirit to break Nishikori - eight years his junior - in the 10th game and seal the second set.
On a roll, Hewitt rattled off a total of five straight games to jump to a 3-0 lead in the third and didn't look back.
Hewitt moved to a 2-0 overall record against Nishikori, who he last defeated at Wimbledon in 2011.
Fit again after a career-threatening toe injury and back in the world top 75 for the first time in three years, Hewitt is suddenly feeling very good ahead of the year's first grand slam.
"I love the battle," Hewitt said of his fightback on Saturday.
"Mentally this is a major win to have come back and gone the distance.
"You do all the hard work in the off season so you don't want to come here and go through the motions.
"You are retired a long time. I want to squeeze out everything I possibly can before then."
Federer is looking to bounce back from a disappointing 2013 in which he failed to make a grand slam final for the first time since 2002.
"I'm very happy to be back in the finals because sometimes it didn't happen so often last year," he said.
"So to start off with a final for me is great, and I hope I can keep momentum up throughout the year, not just next week (at the Australian Open)."