The Perth side will welcome the Tynecastle club - who are expected to be put into administration on Wednesday - to McDiarmid on August 3 for their first top-flight fixture under the auspices of the newly merged set-up.
But despite the fact the entire Jambos first-team squad has been put up for sale, Saints boss Wright is wary of a backlash from their players.
The Northern Irishman, who was unveiled as St Johnstone manager on Tuesday, has experienced the pain of administration during his spell in charge of Distillery in his homeland.
He only left the Lisburn club in 2011 to join Steve Lomas in Perth as his assistant, but saw first-hand the fight the club's insolvency problems inspired in his old team's players.
Wright said: "There is a lot of time still to pass before the first game. Hopefully their financial problems will be sorted out by then.
"Will their situation play any part in our thoughts ahead of the game? No, no, no. I can only focus on my own team and that's what I'll try to do. There might be a lot of press coverage on Hearts between now but I can only prepare St Johnstone for the game.
"I sympathise with the position Gary Locke is in but we will never underestimate anybody. The players and supporters at Hearts deserve a lot of credit for how they have handled the situation, Gary too.
"I had a similar situation myself at Distillery, even though it was only part-time football. The club went into administration and a few of the players had an option to leave. But we held them together and we used it as a motivation to prove people wrong. A lot of folk had us favourites to be relegated but we stayed up.
"The second year we actually got top six and won a cup. So I know you can use it to gel together. The Hearts players have shown in the past what the club means to them and their supporters should take heart from that."