But at home they look especially impregnable after coming through the see-saw seven-goal thriller against St Johnstone on the opening day of the league season. Since then, against Motherwell and Partick Thistle, they have scored five goals, while conceding none. But then this is simply a continuation of the dominance they have enjoyed at home in recent times.
Remarkably, they have lost only one home league game since Thistle themselves were 4-2 victors at Tynecastle two seasons ago. The Glasgow side barely came close to scoring once on Saturday, never mind four times. Who are the next visitors to Gorgie? Only Aberdeen in a particularly mouth-watering prospect.
While there is a lot of football to be played before then, Hearts know the Pittodrie side, who have started their league campaign with four straight victories, will almost certainly provide a stiffer test than Thistle on Saturday. But then Aberdeen manager Derek McInnes will also take note of Hearts’ exceptional home record, while also registering Hearts’ work ethic and physicality.
This is a side being built in the image of Neilson, the head coach, and Craig Levein, the director of football. They are no pushovers. At home in particular, they truly look like kings of their castle. Aside from an enjoyably competitive opening spell, when Thistle looked like having the potential to be tricky customers, there seemed little doubt the points would be remaining in Gorgie.
Osman Sow helped Hearts assert their authority with the opening goal just before the half-hour mark, sweeping home after a strong challenge on goalkeeper Tomas Cerny by Callum Paterson from a corner. Cerny saved Juanma’s second-half penalty but was powerless to prevent the alert Sam Nicholson from netting the rebound. Juanma himself rounded off the scoring with a neat finish after out-muscling Thistle defender Frederic Frans. Cerny helped keep the score down, saving well from Gavin Reilly near the end.
Thistle manager Alan Archibald later wondered whether some of his players had been “overawed” by the occasion, with a sell-out crowd simply adding to the intimidating properties already boasted by Tynecastle’s steep stands. One member of the visitors, Kris Doolan, rejected this, describing the ground as a “great place to play football”. This was particularly the case two days ago, when a big, expectant crowd filed in, relishing the thought of an old fashioned 3pm Saturday kick-off for the first time this season at Tynecastle.
Where Doolan did suggest Thistle were found wanting was in the physical battle with a robust Hearts side. “They are a big team but we have to counteract that,” he said. “We are going to come up against big players in the Premiership. Most teams have lots of big players and Hearts tend to have a wee bit more. We have to be in about them, though, and on Saturday we didn’t do that well.
“It wasn’t the atmosphere,” he added. “Everybody knows what it’s like coming to Tynecastle – we’ve been here before. It’s a great place to come and play football. But we didn’t do that.”
“Not so cuddly anymore” is the tagline adopted by Thistle in an ad campaign supported by their nightmarish new mascot, Kingsley. But they allowed themselves to be bullied by Hearts on Saturday and were, in the end, brushed aside by a team who have now bettered the start made to last season’s Championship title-winning campaign.
Hearts then collected four straight wins but then managed only a draw in their fifth league game, at Dumbarton. They are confounding those who thought it was going to be tougher going for them this time. Of course, it is bound to get a whole lot tougher, with games to come against not only Aberdeen, but also Celtic next month.
Before that clash with Aberdeen, there are three consecutive away trips, starting with tomorrow’s League Cup clash against Forfar, and continuing with games at Hamilton and Inverness.
Ominously for their rivals, Neilson believes Hearts are getting better and better, with plenty of room still left for improvement. Influential performers such as Prince Buaben are still not quite at peak fitness, and there is the suspicion there is still more to come from Juanma, who scored such a fine goal shortly after seeing his weak penalty saved by Cerny.
He, too, looks as though he will benefit from a run of games, while Reilly, an unheralded worker just behind him, is perhaps still getting to grips with the step up from the Championship. Neilson is alert to all this. He suspects his side are still gelling. He also challenged them to be more clinical.
“We have to keep trying to improve,” Neilson said. “Yes, it was a good result. But there are a lot of things we could have done differently. We got into a lot of good areas [against Thistle] and when you play against really good teams, the likes of Celtic, Aberdeen and Dundee United, you get into these areas very rarely. You have to make sure you take the opportunities when you get them.
“At the moment, we are patching people up,” he added. “Buaben and guys like that are sacrificing themselves to get three points for us by playing through injuries. Hopefully we can get to the international break and then get them back ready after that.”
What Hearts would give to reach this interlude with another two victories, making it eight successive league and cup wins. Either home or away, it appears they will take some stopping.