"But if souls have departed this life in faith and love, while nevertheless carrying with themselves certain faults, whether small ones over which they have not repented at all, or great ones for which — even though have repented over them — they did not undertake to show fruits of repentance: such souls, we believe, must be cleansed from this kind of sins" (St. Mark of Ephesus)
The heart was already converted, but it remained with small faults and imperfections that are cleansed away in the furnace of God's loving fire. It is not a conversion after death, but a perfection, like the refining of ore into gold - the substance is not changed but perfected.
There is no "third" state and no temporal purifying fires mentioned anywhere in the Scriptures or teachings of those who understood Greek properly. Some have used Eastern Fathers to show that they agreed with Latins, by incorrectly translating their works. That much is clear from the notes +Mark of Ephesus and other Orthodox Fathers made at the Council in their opposition to the Latin doctrine.
Alexander Kalomiros in his Rivers of Fire, sums up why the Orthodox cannot even conceive of the Purgatory:
"But if souls have departed this life in faith and love, while nevertheless carrying with themselves certain faults, whether small ones over which they have not repented at all, or great ones for which — even though have repented over them — they did not undertake to show fruits of repentance: such souls, we believe, must be cleansed from this kind of sins" (St. Mark of Ephesus)
Hmmm, that seems quite orthodox to me. Sure he wasn't a contributor to the Douay-Rheims Bible?:
1 Cor 3,11 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.
Commentary:
12 "Upon this foundation"... The foundation is Christ and his doctrine: or the true faith in him, working through charity. The building upon this foundation gold, silver, and precious stones, signifies the more perfect preaching and practice of the gospel; the wood, hay, and stubble, such preaching as that of the Corinthian teachers (who affected the pomp of words and human eloquence) and such practice as is mixed with much imperfection, and many lesser sins. Now the day of the Lord, and his fiery trial, (in the particular judgment immediately after death,) shall make manifest of what sort every man's work has been: of which, during this life, it is hard to make a judgment. For then the fire of God's judgment shall try every man's work. And they, whose works, like wood, hay, and stubble, cannot abide the fire, shall suffer loss; these works being found to be of no value; yet they themselves, having built upon the right foundation, (by living and dying in the true faith and in the state of grace, though with some imperfection,) shall be saved yet so as by fire; being liable to this punishment, by reason of the wood, hay, and stubble, which was mixed with their building.