The club believe their midfielder's caution for lashing out at boarding in the Fir Park tunnel last Sunday, which came in the wake of his unjust red card for an altercation with Gretna's Danny Grainger, should now be retracted.
The dismissal was reduced to a yellow card by an SFA appeals panel yesterday, however Stewart remains suspended for tomorrow's SPL meeting with Celtic and is due for a two-match ban beginning December 9 after breaching the 18-point disciplinary threshold.
Hearts have now petitioned for the second yellow card to be retracted on the grounds that Stewart would not have been in the tunnel had he not been issued the red card by referee Mike Tumilty. The appeal will be lodged with the SFA disciplinary committee next week.
Stephen Frail, assistant head coach at Tynecastle, said: "Michael has had his red card reduced to a yellow but I'm not convinced it was even a booking. Had he not been sent off, he wouldn't have been in the tunnel area.
"He has received a one-match ban for what he did but nevertheless, it underlines the need to be really disciplined and the players are aware of that."
Meanwhile, midfielder Eggert Jonsson is an injury concern ahead of tomorrow's Tynecastle meeting Celtic due to an achilles complaint sustained in the draw with Gretna.
"Eggert has to be rated as very doubtful," added Frail. "We won't risk him if it's not 100 per cent. He has been getting treatment all week but he's a doubt. He's our only real concern ahead of the game, which we're all looking forward to."