The defender was also given a red card at the weekend as punishment for using foul and abusive language in the tunnel after the match the Aberdeen was over.
It is understood Wilson had been irked by comments made by members of the Pittodrie squad before the game and delivered a foul-mouthed riposte after his side had secured a win. There is no avenue for appeal - although Wilson will be free to play Raith Rovers in the League Cup tonight - but Hearts have decided to contest McHattie's prospective suspension.
Both clubs are also awaiting a notice of complaint from Vincent Lunny, the SFA compliance officer, following the conduct of Billy Brown, Hearts coach, and Aberdeen manager Derek McInnes, who were embroiled in a heated exchange after the goal which resulted in both being sent to the stand. McInnes has since admitted to pushing Brown and it seems likely that the pair will be offered a two-match touchline ban for their roles in the fracas.
The victory left Gary Locke "absolutely shattered" and also concerned his young side might now begin to stutter after building up impressive momentum in the league. A cup tie with Raith might be considered a reprieve, although Locke does not feel in a position to alter his starting XI.
"I wish I could rest a few players for this game, but I don't think I'm in a position where I could rest anyone," said the Hearts manager. "We've not got a big enough squad to rest anyone, and it's a competition where we're looking to try and get a good run. So, we'll go through there with the squad that's going to get us through the season. In an ideal world I'd love to have rested a few players, but I'm not going to have that option."
That was given as a lament but Gordon Smith is still wary of the threat posed by the Tynecastle side, weary or not. The forward left Gorgie to move to Raith in the summer but has not surrendered the faith he has in his former team-mates to continue to compete this season.
"I know every player in that Hearts squad," said Smith, who was only a fleeting presence in the Tynecastle first team. "I'm not surprised at how the season has gone for them because, for other people, there's a wee bit of the unknown about them.
"The players they're coming up against will not really know how they play, but they're all very fit and fast, and Gary Locke's a good coach and he'll have them up for every game."