The 23 year-old Briton won 7-6 (7-0) 3-6 4-6 6-0 7-5 with the heat reaching 42oC.
This is only the second time Edmund has progressed into the fourth-round of a grand-slam, he got to the fourth round in the US Open two years ago, where he was knocked out by Novak Djokovic.
Edmund described the win as “really good for my career and my confidence going forward”.
Edmund will play in round four in just 48 hours, despite the lack of rest, he remains up-beat:
“I’m pretty confident […] two sleeps until the match. I guess the beauty of Grand Slams is you get that day off.
“It was a key game to get through, and a very long game.”
He will face Ivo Karlovic (Croatia) or Andreas Seppi (Italy) in the next round.