Actually, the blood of Jesus does a thorough job of cleaning us up without a "Purgatory." As far as any residual flaws after Salvation, such as unconfessed sin or unfruitful works, we are told by the Apostle Paul that Jesus will take care of such things at His judgment seat:
For we must all stand before Christ to be judged. We will each receive whatever we deserve for the good or evil we have done in this earthly body. (2 Cor 5:10)
In fact, the only reference to any sin-quenching fire with Biblical credentials is this one:
Because of God’s grace to me, I have laid the foundation like an expert builder. Now others are building on it. But whoever is building on this foundation must be very careful. For no one can lay any foundation other than the one we already have—Jesus Christ. Anyone who builds on that foundation may use a variety of materials—gold, silver, jewels, wood, hay, or straw. But on the judgment day, fire will reveal what kind of work each builder has done. The fire will show if a person’s work has any value. If the work survives, that builder will receive a reward. But if the work is burned up, the builder will suffer great loss. The builder will be saved, but like someone barely escaping through a wall of flames. (1 Cor 3:10-15)
Clearly, this is a judgment before the throne of the Lord, and not an obscure spiritual process occurring in some limbo between heaven and hell. "Purgatory" as doctrine, is neither Scriptural nor necessary.