The Scottish Cup holders gave themselves the rare chance of a back-to-back cup final victories with a semi-final penalty shoot-out win over Inverness at Easter Road on Saturday.
The Jambos will play St Mirren, who pulled off a shock 3-2 win over Celtic on Sunday, in the final at Hampden on March 17.
However, McGlynn wants his players to get ready for a side who, despite being bottom of the SPL, have already beaten the Gorgie men twice this season.
"It will have been a wee while, if anyone at all outside the Old Firm, has done back-to-back cup wins, Scottish Cup and League Cup, so it would be an achievement but that is as far as I would go with it," he said.
"We don't want to get carried away.
"Bradford are in the League Cup final in England and there were a lot of shocks at the weekend.
"Everyone had Celtic as big favourites so I am probably as surprised as everyone else but St Mirren played exceptionally well.
"But the final is March 17, a million miles away and we have so many league games to play between now and then, so the League Cup final goes on the back burner.
"Wednesday night is the priority for me, it is really important because Dundee have beaten us twice and we have had two sore lessons.
"We appreciate that Dundee will be fighting for their lives, they are a few points adrift and won't want to go further adrift.
"Their livelihoods are at stake, if they go down to the First Division, their will be wages cut probably and some players not getting new contracts, so these guys are playing for an awful lot
"But if we don't get a boost from getting through that game against Inverness and getting to a cup final then will you get a boost?"
McGlynn responded to Danny Grainger's claim that he will not be given a new contract at the end of the season when his current deal expires. The defender is out of action for up to nine months after sustaining a knee injury against Motherwell in November.
The former Raith Rovers boss said: "I have the greatest sympathy for Danny, I have said that all along from the minute he got his injury against Motherwell.
"Danny will get all the treatment he needs to get back, Hearts will look after him all the way.
"Danny is like a number of players who find themselves out of contract at the end of the season and he was wanting to know what is going to happen.
"Hearts are cutting back and also with young Kevin McHattie coming through, we wanted a little more time to see if Kevin is able to fill the potential that he has got.
"At this moment in time we are not in a position to say yes to that (giving Grainger a new contract) so I told him if he wants to find a new club he is well within his rights to do that."