Objection 1. It would seem that it is not the same place where souls are cleansed and the damned punished. For the punishment of the damned is eternal, according to Matthew 25:46, "These shall go into everlasting punishment [Vulgate: 'fire']." But the fire of Purgatory is temporary, as the Master says (Sent. iv, D, 21). Therefore the former and the latter are not punished together in the same place: and consequently these places must needs be distinct.
Objection 2. The punishment of hell is called by various names, as in Psalm 10:7, "Fire and brimstone, and storms of winds," etc., whereas the punishment of Purgatory is called by one name only, namely fire. Therefore they are not punished with the same fire and in the same place.
Objection 3. Further, Hugh of St. Victor says (De Sacram. ii, 16): "It is probable that they are punished in the very places where they sinned." And Gregory relates (Dial. iv, 40) that Germanus, Bishop of Capua, found Paschasius being cleansed in the baths. Therefore they are not cleansed in the same place as hell, but in this world.
On the contrary, Gregory says [The quotation is from St. Augustine (De Civ. Dei i, 8)]: "Even as in the same fire gold glistens and straw smokes, so in the same fire the sinner burns and the elect is cleansed." Therefore the fire of Purgatory is the same as the fire of hell: and hence they are in the same place.
Further, the holy fathers; before the coming of Christ, were in a more worthy place than that wherein souls are now cleansed after death, since there was no pain of sense there. Yet that place was joined to hell, or the same as hell: otherwise Christ when descending into Limbo would not be said to have descended into hell. Therefore Purgatory is either close to, or the same place as, hell.
I answer that, Nothing is clearly stated in Scripture about the situation of Purgatory, nor is it possible to offer convincing arguments on this question. It is probable, however, and more in keeping with the statements of holy men and the revelations made to many, that there is a twofold place of Purgatory. One, according to the common law; and thus the place of Purgatory is situated below and in proximity to hell, so that it is the same fire which torments the damned in hell and cleanses the just in Purgatory; although the damned being lower in merit, are to be consigned to a lower place. Another place of Purgatory is according to dispensation: and thus sometimes, as we read, some are punished in various places, either that the living may learn, or that the dead may be succored, seeing that their punishment being made known to the living may be mitigated through the prayers of the Church.
Some say, however, that according to the common law the place of Purgatory is where man sins. This does not seem probable, since a man may be punished at the same time for sins committed in various places. And others say that according to the common law they are punished above us, because they are between us and God, as regards their state. But this is of no account, for they are not punished for being above us, but for that which is lowest in them, namely sin.
Reply to Objection 1. The fire of Purgatory is eternal in its substance, but temporary in its cleansing effect.
Reply to Objection 2. The punishment of hell is for the purpose of affliction, wherefore it is called by the names of things that are wont to afflict us here. But the chief purpose of the punishment of Purgatory is to cleanse us from the remains of sin; and consequently the pain of fire only is ascribed to Purgatory, because fire cleanses and consumes.
Reply to Objection 3. This argument considers the point of special dispensation and not that of the common law.
Source: Summa Theologica (New Advent)