Purgatory and the Cross

I'm struggling to understand the idea behind purgatory.  No, that's not exactly right.  Purgatory, as I understand it, is something of a refining furnace that extracts the impurities from the soul prior to entering heaven.  Those impurities are the results of sin committed by the Christian. The idea then is that Christians, upon death, go to purgatory (or potentially straight to heaven), while non-Christians go to hell.  In the pre-Reformation church, the Roman Catholic pope could authorize indulgences, a transferable certificate that bought or earned less time in purgatory. However, there was really now way to know how long one would be refined in purgatory.  (These same indulgences were one of the fueling fires behind Martin Luther's swing toward reformation.)

So more accurately, what I don't understand is how purgatory lines up biblically with the cross.  The idea of purgatory is a mockery of the cross.

To the issue of purgatory and daily blasphemies needed to prop it up, John Calvin says,
"We are bound, therefore, to raise our voice to its highest pitch, and cry aloud that purgatory is a deadly device of Satan; that it makes void the cross of Christ; that if offers intolerable insult to the divine mercy; that is undermines and overthrows our faith.  For what is this purgatory but the satisfaction for sin paid after death by the souls of the dead? Hence when this idea of satisfaction is refuted, purgatory itself is forthwith completely overturned.  But if it is perfectly clear, from what was lately said, that the blood of Christ is the only satisfaction, expiation, and cleansing for the sins of believers, what remains but to hold that purgatory is mere blasphemy horrid blasphemy against Christ?  I say nothing of the sacrilege by which it is daily defended, the offenses which it begets in religion, and the other innumerable evils which we see teeming froth from that fountain of impiety" (John Calvin, Institutes of the Christian Religion, Book 3, Ch 5, Sec 6.) 
I realize my statements here may be offensive to my Roman Catholic friends.  I am open to conversation on this topic, but I make no apology.  I hope that there is a mutual realization that purgatory is offensive to the Protestant understanding of passages such as Romans 5:8, Romans 8:1, Hebrews 9:25-28, 2 Corinthians 5:21, Isaiah 53:6, and Philippians 1:23.

*Painting by Ludovico Carracci is in the public domain.