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The concept of nothing impure entering Heaven is one indirect prooftext of Purgatory; the phrasing in the discourse on some sins being not pardonable even in the life to come (Mt 12:32) would make no sense unless there are sins that are forgiven only in the life to come. Also, the parable of the unmerciful debtor depicts a punishment for sin that is temporal, "until the last farthing is paid".

But none of that would be decisive if it were not for 1 Cor 3, where a man is likened to a building which stands on the foundation of Christ. Such man is saved, but not until the imperfections in his soul are burned off. Note that this purification doesn't start till all his works are "made manifest", hence after his death. This is the idea of purgatory in its essence: the temporary place state of purification of a soul whose sins have already been forgiven through the superabundant merit of Christ.

Here is this passage in Douay translation:

8 ...And every man shall receive his own reward, according to his own labour. 9 For we are God's coadjutors: you are God's husbandry; you are God's building. 10 According to the grace of God that is given to me, as a wise architect, I have laid the foundation; and another buildeth thereon. But let every man take heed how he buildeth thereupon.
11 For other foundation no man can lay, but that which is laid; which is Christ Jesus. 12 Now if any man build upon this foundation, gold, silver, precious stones, wood, hay, stubble: 13 Every man's work shall be manifest; for the day of the Lord shall declare it, because it shall be revealed in fire; and the fire shall try every man's work, of what sort it is. 14 If any man's work abide, which he hath built thereupon, he shall receive a reward. 15 If any man's work burn, he shall suffer loss; but he himself shall be saved, yet so as by fire.
(1 Cor. 3)

The explanation that Protestants give is that the passage speaks of extra rewards that some of the elect get according to their good works, in addition to justification given for their faith, but that is merely reformulating the same doctrine in terms of losing a reward rather than suffering through purification. No matter how we call this state, it is clear that it is a state that follows natural death, involves some kind of suffering, available to the saved only, and has purification (removal of base material) as its end.