I have done quite a bit of studying on purgatory and from what I have read purgatory is basically (if you want to put it in dimensional terms) right above hell. In fact some of the Saints and mystics tell us that the fires of purgatory are the same as those of hell, that they are fueled by the fires of hell, but that of course is in the lowest parts of purgatory, and the only difference is that in purgatory there is light, the light of salvation, of the knowledge that the beautific vision awaits, while in hell there is nothing but darkness and despair.
So purgatory is broken down into sections with the lowest part being of course the most dreadful and the highest being that basically the only thing you suffer is the lack of the beautific vision. Don’t get me wrong I say “only” but from the mystics to the saints we are told that the worst part of purgatory is the seperation from God, it is a pain that is indescribable.
Now we are also told that the souls there refuse to leave purgatory until their sins have been completely expiated. In fact one of the mystics told it like this that the souls in heaven and God Himself would allow souls into heaven saying "don’t worry we are compassionate, merciful and loving. No one will say anything about the stench filled or muddy soul that you have, but the soul itself refuses to come into the presence of God until God has allowed it to be properly prepared.
The pains of purgatory are of course in line with the sins committed, thirst, hunger, the torture of the tongue, are a few of what is mentioned, but one thing that I found interesting was the description that there were basically two sides of a certain part of purgatory, one was the fires and the other was an equally indescribable cold or ice. That the souls suffering there would hurl themselves from the fire to the ice hoping for relief, but finding none. The only relief comes from our prayers, masses said, and when the Blessed Mother is in purgatory. Many saints and angels visit purgatory including St Michael and St Joseph and yet the pain continues, however when the Blessed Mother enters there is no pain anywhere for any soul.
Anyway, I could go on and on but there are many more well qualified and more knowledgeable authors out there. The first book that got me interested and really into studying purgatory is called “The Dogma of Purgatory”. I suggest it, but I warn you, it is not an easy read, it is not a light read, and it is an emotional read. Once read you will want to know more, you will study purgatory throughly and you will end up spending or wanting to spend a lot more money on masses and time in prayer for the Holy Souls in Purgatory.