Since then, they have been striving for consistency at the top end of the league standings and while there have been a further four second or third place finishes, the best they were able to follow any of them up with was fourth best, in 2006/07.
On the other occasions they had to settle for fifth and sixth spots, illustrating just how difficult it is to replicate the form needed to metronomically deliver week in, week out over the course of a demanding campaign.
“There are a lot of contributing factors in that,” insists Craig Levein, the last man to oversee a Tynecastle side proving themselves best of the rest in successive seasons, when his 2003/04 squad repeated the league achievements of the 2002/03 campaign.
“The very nature of finishing third means you have Europe to consider as well when it comes to the second season, and that combination of playing in Europe and still finding a way to perform in the various domestic competitions is very difficult.
“You need to have enough good players in the group to ensure a version of success in the European arena while still maintaining standards and performing really consistently in the league.
“That is a big ask. It is not easy because if you do well in the initial season it is often the case that you lose two or three of your best players to the Old Firm or to clubs in England. The fact you finish third shows that you are going well and that is when predators appear on the horizon.”
Such was the case this summer as defender John Souttar headed west to join up with Rangers, while striker Ellis Simms’ performances in helping Hearts seal third spot alerted a number of English sides to his potential as parent club Everton consider his next loan move.
“When you do well you are almost guaranteed to lose some players that you don’t want to lose and that makes the second season tough because there are so many demands, people see you as a scalp and you need to have enough players there to compete on two fronts,” Levein added.
That is where recruitment and mindset is so crucial as quality and quantity need to harmonise.
Well aware of the requirements, the club have been active over the summer, bringing in Alan Forrest, Lewis Neilson, Kye Rowles, Jorge Grant and Lawrence Shankland, while also turning Alex Cochrane’s successful loan spell into a permanent deal. But manager Robbie Neilson, who was an integral part of the 2002-2004 playing squads, along with current captain and goalkeeper Craig Gordon, knows that even more strength and depth will be key to achieving his ambitions for the coming term.
Hoping to bring Elliot Anderson to Gorgie on loan, he was disappointed to be told that the Newcastle United attacking midfielder will be staying at St James Park, but highlighting the need to rely heavily on the squad rather than the same eleven players each game, he said the club will now turn attention to corralling a number of other targets as they bolster options.
The league campaign gets underway on Saturday when they host Ross County, while newly-promoted Kilmarnock provide the opposition when the capital side kick-off their League Cup involvement late next month. By then they will already be up and running in UEFA competition as well and will know whether they have Europa League or Europa Conference League games to look forward to.
“I think Hearts are capable,” stressed Levein. “The interesting thing will be how the European games affect things. Doing well in Europe and still having the energy - mental and physical - to sustain things on the domestic front will be a challenge.
“And, until the transfer window shuts, we won’t really know just how prepared they are. But one thing I do think about Robbie, or Robbie and Joe [Savage, Hearts’ sporting director], is that their recruitment has been bang on.
“They did well bringing Simms in last season and the Australian boys they have identified have been able to come in and hit the ground running, so if they can maintain that success rate when it comes to signings and they get the numbers they are looking for then the chances of being successful on two fronts are good, but if they can’t get the numbers they need then the chances are very, very slim.”
And, other factors become relevant in that recruitment process. A squad already possessed of international calibre, the addition of more capped individuals like Rowles will be an advantage, according to Levein.
“When you bring players in it helps to bring in international players because they have some idea what it’s like to have the emotions of an international match, which is akin to a big European game, and then come back to play for your club and to be able to get your energy back and not turn up feeling emotionally drained.
“I certainly felt that myself when I first started playing European matches. I was knackered when I came back to play at weekends but over a period of time you get used to that so the more players who have that experience, the better.”
While Europe remains something of an unknown quantity, in the Premiership, Levein does expect a greater challenge from the chasing pack, believing Hibs and Aberdeen can only improve on last term, while Dundee United will be attempting to close the gap.
But there is a significant void to bridge, in terms of the points tally and goal difference and unless the others sufficiently get their act together, Hearts will have room for one or two slip ups as they get into the rhythm of successfully juggling team line-ups, squad rotation and foreign and homegrown demands.