United's football manager, Ante Kovacevic, told The World Game the club had applied to FFA for a delay and was anticipating a decision from the governing body before the weekend.
The forecast is for a top of 40 degrees celsius in Adelaide on Sunday.
The round-nine game at Coopers Stadium is scheduled for a 4.30pm local time kick-off and adding to concerns is the fact there is a round-eight W-League game between the same two clubs scheduled for 1.30pm at the same ground.
"We've aired our concerns about the game with the FFA," Kovacevic said. "We saw the recent situation in Perth and we want to try and avoid that and see if there can be any movement, but obviously there are other key stake-holders to consider."
Kovacevic was referring to the round-seven game in Perth on November 21 between Glory and Sydney FC. It was a 4.30pm kick-off with the temperature at 34 degrees and players from both sides struggled in the heat. The result was a poor-quality game that finished 0-0.
Asked how FFA had responded to Adelaide's concerns, Kovacevic replied: "It's under consideration, so the ball's in their court. There's not much else we can do but wait to see what happens now.
"They'll be looking into the possibility of delaying the game. They're aware of our concerns and I believe Perth Glory have made their concerns known as well, and obviously there's the women's game before us.
"That's even more concerning for them, because they're playing in the middle of the day when there will probably be zero shade for the players (from the grandstand).
"The FFA said they would talk about it internally and get back to us, but we have asked for a delayed kick-off and we hope to know if that will happen before the weekend.
"Once we saw the predicted temperature we raised our concerns. We've had discussions with the FFA over the last couple of days."
Kovacevic said he couldn't be sure whether any consideration would be given to postponing the women's game or shifting it to another venue, or whether any delay would simply mean the women's game starting closer to the originally scheduled men's time and the men's game later.
"We're not too sure," he said. "The FFSA runs our women's team, so they've been in communication with the FFA. That's out of our hands, but I believe that whatever happens both games will still be played on the weekend.
"The first port of call for us is to try to get a decision made on delaying the kick-off. A new starting time would be in conjunction with FFA and I presume the broadcaster as well, and the two women's teams.
"You would like to think Fox Sports would be sympathetic to the cause to ensure they get a better product to show on TV, rather than a game that is badly affected by heat. It would be of benefit to them as well."
The Adelaide club released a statement on Thursday that read in part they had: "been in direct contact with a number of Adelaide United members and supporters regarding this (heat) issue and we sympathise and understand the concerns being raised".
The statement continued: " From the Club’s point of view, the welfare of the players and spectators is, and will always be, paramount. We’ve had numerous conversations with the FFA of the possibility of a time change, but we will update members, sponsors, and fans accordingly as to any possible changes that could take place."
Also in the statement, Adelaide chairman Greg Griffin appealed to the club's Red Army fan group to commit to supporting the team for the entire game.
The Red Army declared on Thursday morning that it would be walking out after 30 minutes to play its part in protests against the FFA's recent treatment of active supporters over the ban appeal policy drama.
"While we understand the Red Army’s position and stance on matters from earlier today, from the club’s perspective, we do not want to see our players adversely impacted by the possibility of a smaller attendance at Coopers Stadium, especially at such a crucial time for us," Griffin said.