Temperatures topped out at 42.2 degrees Celsius at 5.45pm, just after Murray began his first-round match against Japan's Go Soeda, which he went on to win 6-1 6-1 6-3.
The pair were fortunate that Hisense Arena is one of the stadium courts, so they were at least able to play in shade.
Canadian player Frank Dancevic and a ball boy both collapsed on court while China's Peng Shuai vomited then suffered cramp during her defeat by Kurumi Nara.
The tournament implemented part of its extreme heat policy, with women being given a 10-minute break between the second and third sets, but they decided not to put it fully into operation, which would have seen play suspended and roofs on show courts closed.
Dancevic described the conditions as "inhumane", adding: "Having players with so many problems and complaining to the tournament that it's too hot to play, until somebody dies."
Murray said: "It's definitely something that you maybe have to look at a little bit. As much as it's easy to say the conditions are safe - a few people said there's doctors saying it's fine - it only takes one bad thing to happen.
"And it looks terrible for the whole sport when people are collapsing, ball kids are collapsing, people in the stands are collapsing. That's obviously not great.
"I know when I went out to hit before the match, the conditions at 2.30 or 3pm were very, very tough. Anyone's going to struggle in that heat.
"There's been some issues in other sports with players having heart attacks. I don't know exactly why that is. In this heat, that's when you're really pushing it to your limits. You don't want to see anything bad happen to anyone."
When to stop matches is at the discretion of referee Wayne McKewen after a rule change this year, and based on readings not just of temperature but also humidity and wind.
Murray said: "Apparently it wasn't that humid today. That's why it wasn't implemented. There's different rules for the men and women, I don't know why.
"I didn't sit down and discuss whether the guys are happy with the rules or not. But every singles person that I saw coming in from practice or going out to play a match or coming back from a match, everyone just said, 'It's really hot today'."
In a statement, chief medical officer Tim Wood said: "The majority of matches were completed without any court calls from the medical team.
"Of course there were a few players who experienced heat-related illness or discomfort, but none required significant medical intervention after they had completed their match. Generally the playing group coped extremely well."
None coped better than Murray, who was playing only his third competitive match following back surgery but was detained for only an hour and 27 minutes by Soeda.
The world number 112 was clearly not in the Wimbledon champion's class, but there was no doubt the fourth seed was striking the ball extremely well.
After two aces helped Soeda hold serve to start the match, Murray reeled off nine games in a row. The third set was a bit scrappier but by then the hard work was done.
Murray said: " I played well today. Practice the last week or so was very good. I played with a lot of good players and hit the balls very well on the courts here.
"I maybe didn't expect to play as well as I did today, but the signs have been good in practice. I started the match off very well and did everything solid."
In the second round Murray will play French qualifier Vincent Millot, who saw off American Wayne Odesnik in five sets for his first grand slam win.
The forecast is for temperatures to exceed 40C until the weekend.