The Scot, who is due to face the world number two in a semi-final showdown should he defeat Jeremy Chardy, has played three of his four matches in the afternoon heat of Melbourne.
His quarter-final with the Frenchman will be his fourth day match, while his clash with Gilles Simon started late in the afternoon in slightly cooler conditions.
According to the Daily Mail, Murray's camp believe that television broadcaster Channel 7 has too much input in the scheduling, with Ivan Lendl reportedly making his frustration clear to event organisers.
Federer has already played matches against Nikolay Davydenko, Bernard Tomic and Milos Raonic at night, while his quarter-final clash with Jo-Wilfried Tsonga is also scheduled for the cool of the evening.
Tournament director Craig Tiley said that he has spoken to Murray's camp, who "understand" the situation.
"Television has a contributing voice," said Tiley. "There are eight of us in scheduling meetings and we calculate that we have to take into consideration probably more than 20 variables.
"I've spoken to the Murray camp and they understand, they know what goes on at the scheduling."
Federer's first-round match with Benoit Paire has been his only match in the day so far.