Shaun Saunders' team were handed the deduction - which could cost them the Southern Combination Football League Premier Division title - on May 22 after an SCFL disciplinary committee gave them the maximum punishment after they played Melford Simpson while he was suspended.
Heath were hoping then they would get a 'lenient' punishment from the SCFL after the FA warned them about their future conduct in a previous FA hearing.
After the SCFL handed out the punishment, the club lodged an appeal to FA and they will find out their fate at the hearing at Wembley.
After they were handed the punishment in May, secretary Mark Russ said: "I think the word is gutted. I am numb, I really am numb.
"As far as I am concerned, a reasonable person based on the facts that we presented, I think we have presented there were exceptional circumstances and that’s what we will hopefully appeal to."
Heath finished the season four points above second-placed Shoreham.