Those who don't repent also don't believe, so who exactly is "flamed" to pristine purity in this mysterious state called the Purgatory? For, if they feel God's fire not as loving warmth but as unbearable burning, it is because they hate Him.
The way you describe the Purgatory leaves two possibilities -- either God purifes those in the Purgatory through His will and against theirs, or they change their mind once Love sears their wicked souls. So regardless which one you choose, it seems not to be a conversion in the heart but extortion under duress.
The consensus patrum of the Eastern Fathers certainly did not include any "place" called or like purgatory. The image of God's Love as a purifying or tormenting fire is present, though and the image of fire is found throughout their writings.
"Do not deceive yourself, God is fire and when He came into the world, and became man, He sent fire on the earth, as He Himself says; this fire turns about searching to find material — that is a disposition and an intention that is good — to fall into and to kindle; and for those in whom this fire will ignite, it becomes a great flame, which reaches Heaven. ... this flame at first purifies us from the pollution of passions and then it becomes in us food and drink and light and joy, and renders us light ourselves because we participate in His light." Saint Symeon the New Theologian (Discourse 78).
Saint Basil says that "...the sword of fire was placed at the gate of paradise to guard the approach to the tree of life; it was terrible and burning toward infidels, but kindly accessible toward the faithful, bringing to them the light of day."
"I say that those who are suffering in hell, are suffering in being scourged by love. ... It is totally false to think that the sinners in hell are deprived of God's love. Love is a child of the knowledge of truth, and is unquestionably given commonly to all. But love's power acts in two ways: it torments sinners, while at the same time it delights those who have lived in accord with it." Saint Isaac the Syrian (Homily 84)
As to the Final Judgment, Archbishop St. John Maximovitch, in The Last Judgement, Orthodox Word (November-December, 1966): 177-78, though not a Father, wrote:
"“The end of the world” signifies not the annihilation of the world, but its transformation. Everything will be transformed suddenly, in the twinkling of an eye. ... And the Lord will appear in glory on the clouds. Trumpets will sound, and loud, with power! They will sound in the soul and conscience! All will become clear to the human conscience. The Prophet Daniel, speaking of the Last Judgement, relates how the Ancient of Days, the Judge, sits on His throne, and before Him is a fiery stream (Dan. 7:9-10). Fire is a purifying element; it burns sins. Woe to a man if sin has become a part of his nature: then the fire will burn the man himself.
‘This fire will be kindled within a man: seeing the Cross, some will rejoice, but others will fall into confusion, terror, and despair. Thus will men be divided instantly. The very state of a man's soul casts him to one side or the other, to right or to left.
‘The more consciously and persistently a man strives toward God in his life, the greater will be his joy when he hears “Come unto Me, ye blessed.” And conversely the same words will call the fire of horror and torture on those who did not desire Him, who fled and fought or blasphemed Him during their lifetime!
‘The Last Judgement knows of no witnesses or written protocols! Everything is inscribed in the souls of men and these records, these “books”, are opened at the Judgement. Everything becomes clear to all and to oneself.
‘And some will go to joy, while others — to horror.
‘When “the books are opened”, it will become clear that the roots of all vices lie in the human soul. Here is a drunkard or a lecher: when the body has died, some may think that sin is dead too. No! There was an inclination to sin in the soul, and that sin was sweet to the soul, and if the soul has not repented of the sin and has not freed itself from it, it will come to the Last Judgement also with the same desire for sin. It will never safisty that desire and in that soul there will be the suffering of hatred. It will accuse everyone and everything in its tortured condition, it will hate everyone and everything. “There will be gnashing of teeth” of powerless malice and the unquenchable fire of hatred. ‘A “fiery gehenna” — such is the inner fire. “Here there will be wailing and gnashing of teeth.” Such is the state of hell.’"
"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.