Cummins scored the only goal of the game but was booked in the first half for going to ground too easily as he tried to manoeuvre around Jambos centre back Igor Rossi.
Kane was booked in the second period for a similar act as he tried to skip past Faycal Rherras.
It was a cruel bit of irony for Saints boss Wright, who was outspoken in the build-up to the match regarding Hearts’ tendency to “maximise contact” in order to win fouls.
He insisted the club would fine both players if they were guilty of simulation, but after studying footage he’s decided instead to appeal both yellow cards.
He told the Dundee Courier: “There is no reason for me to go fining the pair.
“There is certainly enough for us to give notice of appeal for both yellow cards.”