Aussie Ash Barty was far luckier, playing in the evening against Italian Camila Giorgi.
Although many expected a tight contest, Sharapova cruised to victory and won in straight sets.
"We're high-level athletes capable of pushing the limits very far and sometimes too far, that's why I say that it could be risky".
According to the Daily Mail newspaper, which first reported the meeting on Monday, Djokovic was said to have asked all non-players to leave the room and then gave a lengthy speech from the stage about forming a players' union, accompanied by an Australian lawyer.
"I love Australia. I love the summer time".
"But for me it wasn't sort of an issue today ... sort of fortunate not to get in the middle of the day".
"I did say the first two matches you're going to see who's doing well and not so well".
After beating Monfils in a sloppy, four-set slug-fest, Djokovic said tournament supervisors should have delayed the match. He will now face Germany's Maximilian Marterer in the third round.
Monfils appeared to struggle more than the six-time champion in the searing heat, his game falling off after an impressive start to allow Djokovic to fight back.
I'm Proud of You
Some are speculating the Mallette's message might be in response to her son's beau's mother's (keep up now) comments. No matter how hard you try to advise.
None of the top seeds or comeback men failed, but all had to bear the brunt of Melbourne heat with temperatures soaring above the 40 degree Celsius mark.
"It was tough to breathe ..."
"I got super dizzy". I think that was a good test for him.
The drama comes after Monfils became distressed during his second-round loss to Djokovic.
"I think physically it was obvious that you just have to try to hang in there".
Meanwhile, there were several upsets as Milos Raonic and Roberto Bautista Agut were knocked out by Lukas Lacko and Fernando Verdasco, respectively; in the women's draw, Andrea Petkovic beat Petra Kvitova 6-3, 4-6, 10-8 in a three-hour epic.
"There is a rule [that we use] about index, combination between temperature and humidity", he said. But I think there is a limit, and that is a level of I guess tolerance between being fit and being, I think, in danger in terms of health.' Asked if the ATP should take a cue from the WTA about changing the venue for the ATP World Tour Finals, Djokovic replied: 'I need to congratulate them.
Del Potro beat Karen Khachanov in four sets before he too complained about the weather.
Courier - the former No. 1 and Australian Open victor - told Djokovic he would limit his questions so the 30-year-old could escape the heat, prompting this reply: "You can ask me as many questions as you want in the locker room, ice bath".
Tournament director Craig Tiley said the Australian Open was one of the only events in the world to actually have a heat policy.