With third spot already secured, Hearts can enjoy their trip to St Mirren on Wednesday night without too much pressure.
But who should make Steven Naismith's starting line-up?
Put yourself in the manager's shoes and pick your XI here.
Watch Sportscene analysis of Lawrence Shankland's goal against Dundee - his 30th of the season.
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Jonathan Sutherland
Sportscene presenter
Hearts cruised past Dundee on Saturday, and have two players in my team of the week.
Kye Rowles was consistent at the back and the Australian international contributed well to another clean sheet for Hearts.
Up the other end, Barrie McKay turned in an eye-catching display. On his day he has the vision and class to make all the difference.
Image source, SNSHearts head coach Steven Naismith has backed young striker James Wilson to be a "big player" for the club moving forwards.
The 17-year-old made his league debut in Saturday's 3-0 win over Dundee, and Naismith says he has had to work hard for the opportunity.
“Young players will get opportunities here but they are not just going to get given opportunities for the sake of it,” Naismith said.
“James has had to be patient, he’s been frustrated at times that he’s not had a chance and not been able to get in but I’ve lived it as a young player and I understand it.
“If he goes in too early his confidence can take a drop which then takes four months to get back to where he was.
“We need him to have a steady rise and going forward he will be a big player like Macaulay Tait and Aidan Denholm this season.”
Watch highlights as Hearts beat Dundee in the Scottish Premiership.
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Image source, SNSBarrie McKay says he doesn't want this season to end after the Hearts winger played a starring role in Saturday's 3-0 win over Dundee.
The 29-year-old has been limited to just 14 appearances in all competitions in an injury-hit campaign, but he looked back to his best against Dundee, setting up two of the goals.
“It’s been a difficult season," he told BBC Scotland. "With injury, then coming back and the injury again.
"Hopefully I’ve seen the end of it now and I’m enjoying my football. [The season's end] is probably coming at the wrong time for me but the boys have been brilliant.
“I’m just glad I can come in now and help out."
We asked for your thoughts after Hearts beat Dundee 3-0 at Tynecastle in the Scottish Premiership.
Here's what you had to say:
David: The ball winning efforts of Beni Baningime and Cammy Devlin are so important to the team. I hope they both get new contracts.
Don: A nice easy win and it was good to see youngsters getting a run out. James Wilson showed why some English outfits have had their eye on him in the past. Altogether a good day for Hearts.
Anon: Steven Naismith has got us in a good place. Goal-scorers up front and a secure defence. We are able to field a good side and still have a quality bench. Financially secure and a European campaign to come.
Steven: A really good performance. Naismith deserves a real amount of credit because this current squad is looking like it’s going to become a proper football team. They can play well and win and they can play poorly and still get a result. For years we’ve been a soft touch at times but this side really looks the real deal.
Image source, SNSHearts have kept a clean sheet in 16 of their 36 games, only Rangers (18) have done this more often in the Scottish Premiership this season.
L. Shankland has scored 22 goals this season (one in this game), more than any other player in the Scottish Premiership.
Dundee have lost their last three games in the Scottish Premiership, their last longer losing streak was from 4th December 2021 to 18th January 2022, a run of six games.
Hearts head coach Steven Naismith: "Good performance, clean sheet first of all. We were secure out of possession. When we started moving the ball quicker in the second half, we created more chances and we scored some good goals so, yeah, pleasing afternoon.
"[Barrie McKay's] quality is there. He's still not fit so that's a work in progress. He's got unbelievable quality. We rotated the team and we will do the rest of the week. We trust every player that plays."
Were you at Hearts' 3-0 win over Dundee or following the match from home? Either way, we want your views on the game – have your say here.
With this, a 20th win from 36 in the league so far, Hearts showed once again why they are the envy of similarly-resourced Aberdeen and city rivals Hibernian.
Options such as Alan Forrest, Barrie McKay and Kenneth Vargas, in addition to top scorer and PFA Scotland player of the year Lawrence Shankland, mean Steven Naismith's side will always create chances but their defensive prowess is just as impressive.
Only Celtic and Rangers have conceded fewer goals this term.
Dundee sustain a third top-six defeat out of three and are in danger of seeing their impressive season fizzle out.
Still, the Dens Park side still have lots to boast about after a top-half finish on their return to the Premiership.
It's been an injury interrupted season for Hearts winger Barry McKay but he showed what he has to offer with two assists.
Image source, SNSMcKay (left) with Lawrence Shankland
Goalkeeper Craig Gordon returns to the Hearts starting line-up as Zander Clark drops to the bench while Alan Forrest and Barrie McKay also comes into the starting line-up at the expense of Frankie Kent and Jorge Grant, who both make the bench.
Dundee also make three changes. Ryan Astley, Malachi Boateng and Michael Mellon start in place of Rickie Lamie, Scott Tiffoney and Mohamed Sylla. Tiffoney and Sylla are among the substitutes.
Hearts: Gordon, Lembikisa, Rowles, Cochrane, Kingsley, Forrest, Devlin, Baningime, McKay, Shankland, Vargas, .
Substitutes: Clark, Kent, Grant, Oda, Sibbick, Denholm, Fraser, Tagawa, Wilson.
Dundee: McCracken, Donnelly, Astley, McGhee, Portales, Dodgson, Cameron, Boateng, McCowan, Mellon, Bakayoko.
Substitutes: Sharp, Tiffoney, Main, Mulligan, Robinson, Robertson, Holwey, Sylla, Costelloe.
Image source, SNSCalem Nieuwenhof, Liam Boyce (both hamstring), Craig Halkett and Peter Haring (both knee) all remain sidelined for Hearts.
Dundee boss Tony Docherty had no fresh injury worries. Captain Joe Shaughnessy had a successful operation on his knee on Monday and Owen Beck (groin) is also out for the season.
Image source, SNSLawrence Shankland deserves all the prizes and plaudits coming his way, says Hearts head coach Steven Naismith.
Shankland became the first Hearts player ever to win the PFA Scotland Premiership player of the year award last weekend, having scored 21 league goals so far this season.
The Scotland striker is also in contention to win the Scottish Football Writers’ Association player of the year award, alongside Celtic's Matt O'Riley, Rangers keeper Jack Butland and Aberdeen striker Bojan Miovski.
“I expected him to win it and I think he will win them all," Naismith said. "That’s because he deserves them.
“The parts that come out after of him being the first Hearts player ever to win that award tells you the magnitude of it.
“If you look at the roll of honour of these awards, it is 80-90 per cent Old Firm players. Inevitably, because they are in squads that are valued higher, they create more chances, they dominate more games.
“For Lawrence to do what he has done, not just this season but last season, shows you his level of consistency, shows his determination, shows his quality. As he has got older he has got much better as a player.
“It’s a brilliant, brilliant achievement, for him personally but for us as a squad to have the guy who has scored all those goals and got player of the year. It shows we have been doing stuff right all season.”
Image source, SNSJack Butland, Bojan Miovski, Matt O'Riley and Lawrence Shankland have been named on the shortlist for the Scottish Football Writers' Association player of the year award.
Hearts striker Shankland will be looking to add to his PFA Scotland Premiership player of the year prize, having already pipped Rangers' Butland and O'Riley of Celtic to the award.
Miovski, who has scored 24 goals for Aberdeen this term, was omitted from the PFA's nominees, with Rangers captain James Tavernier included.
But having been a rare highlight in a disappointing season at Pittodrie, the Macedonian has carried a struggling side on his back and made his mark in Europe, as well as against the Old Firm.
Butland has enjoyed a stellar first campaign north of the border, filling the sizeable gloves left behind by Rangers legend Allan McGregor with authority this season.
The Englishman has kept 18 clean sheets in 35 Premiership games and has helped the Ibrox side boast the best defensive record in the top flight, conceding just 25 times.
On the other side of Glasgow, midfielder O'Riley has enjoyed his most productive season in green and white, racking up 12 goals and 14 assists - a league high.
With Callum McGregor and Reo Hatate missing at times, the Denmark international has stepped up this season and his impact could see Celtic retain their title despite increased pressure from their rivals.
But as the Premiership top scorer and with one award already claimed, Shankland could be the man to beat.
While his goals have rightfully grabbed the headlines, the 28-year-old has also been crucial in Hearts' build-up play en route to third place and has taken the role of captain in the absence of Craig Gordon.
Image source, SNSHearts have won their last two league games against promoted sides in the Scottish Premiership (both v Dundee), and last won three in a row against such opponents in the top flight in 2011-12, when they beat Dunfermline Athletic three times in succession.
Dundee have lost both of their last two league meetings with Hearts, last losing more in a row against them in the top-flight in October 2004 (4 in a row).
Hearts are unbeaten in nine home league games (W6 D3), last going 10+ without defeat within a single Scottish Premiership season on home soil from November 2017 to April 2018 (12).
Dundee have lost their last two league games, last losing more in a row in the Scottish Premiership from December 2021 to January 2022 (six).
Lawrence Shankland has scored in five of his last six league appearances at Tynecastle for Hearts (five goals), also providing three assists in his last two such matches.
Brian McLauchlin
BBC Sport Scotland Senior Reporter
Third place in the league achieved. Job done.
Although defeat at Celtic Park last weekend was a disappointment, the primary goal has been achieved in what has been a long, at times arduous season but ultimately one everyone at Tynecastle can look back on with great pride.
So how do Hearts improve on the achievements of this campaign?
Well, winning a piece of silverware would be a start. You have to go back to May 2012 for the last time Hearts lifted the Scottish Cup and in doing so gave everyone associated with the club a day they will remember for a lifetime.
You have to go even further back to find the last time the League Cup was lifted. That was season 1962-63 when the Jambos defeated Kilmarnock 1-0 with Norman Davidson scoring the only goal in front of 51,000 at Hampden.
And then of course there is Europe. Hearts will enter the Europa League in the play-off round at the end of August. Come through that tie, which will be tricky, and a further eight matches in the new format of the competition will beckon.
Defeat, however, will bring the bonus of another crack at the Conference league.
But there are still things to achieve in this campaign. Reaching 70 points would be remarkable and an indication that things really are on the up.
Dundee at home on Saturday are first up before attention the turns to St Mirren and a final game of the season at home to Rangers.
The sombrero will have to wait as work remains to be done.
Hearts host Dundee in the Scottish Premiership on Saturday as they look to bounce back from defeat to Celtic.
Should Steven Naismith make changes to the side that secured third place but lost in Glasgow?
Pick your Hearts XI for the game here.
Steven Naismith is adamant he won't destroy squad unity at Heart of Midlothian by bloating the squad to tackle the demands of European football. (Daily Record)
Read the rest of Wednesday's gossip.
Image source, BBC Sport
