Pergatory is actually another good example of a Catholic innovation that is fairly easily justified from the Bible.
Here is New Advent:
newadvent.org/cathen/12575a.htm
It provides the relevant Biblical citations. But the key thing to note is that belief in pergatory requires something more than a text search of the Bible. It requires logical inference.
So did the Christians of Acts believe in pergatory? Probably not.
Guess again, Bubba:
Clement of Alexandria
The believer through discipline divests himself of his passions and passes to the mansion which is better than the former one, passes to the greatest torment, taking with him the characteristic of repentance for the faults he may have committed after baptism. He is tortured then still more, not yet attaining what he sees others have acquired. The greatest torments are assigned to the believer, for God’s righteousness is good, and His goodness righteous, and though these punishments cease in the course of the expiation and purification of each one, “yet” etc. (
Patres Groeci. IX, col. 332
A.D. 150-215]).
Origen
If a man departs this life with lighter faults, he is condemned to fire which burns away the lighter materials, and prepares the soul for the kingdom of God, where nothing defiled may enter. For if on the foundation of Christ you have built not only gold and silver and precious stones (I Cor., 3); but also wood and hay and stubble, what do you expect when the soul shall be separated from the body? Would you enter into heaven with your wood and hay and stubble and thus defile the kingdom of God; or on account of these hindrances would you remain without and receive no reward for your gold and silver and precious stones? Neither is this just. It remains then that you be committed to the fire which will burn the light materials; for our God to those who can comprehend heavenly things is called a cleansing fire. But this fire consumes not the creature, but what the creature has himself built, wood, and hay and stubble. It is manifest that the fire destroys the wood of our transgressions and then returns to us the reward of our great works. (
Patres Groeci. XIII, col. 445, 448
A.D. 185-232]).
Tertullian
That allegory of the Lord [Matt. 5:25-26] . . . is extremely clear and simple in its meaning . . . [beware lest as] a transgressor of your agreement, before God the judge . . . and lest this judge deliver you over to the angel who is to execute the sentence, and he commit you to the prison of hell, out of which there will be no dismissal until the smallest even of your delinquencies be paid off in the period before the resurrection. What can be a more fitting sense than this? What a truer interpretation? (
The Soul 35
A.D. 210]).
The faithful widow prays for the soul of her husband, and begs for him in the interim repose, and participation in the first resurrection, and offers prayers on the anniversary of his death (
Monogamy 10
A.D. 213]).
Cyprian
It is one thing to stand for pardon, another thing to attain to glory; it is one thing, when cast into prison, not to go out thence until one has paid the uttermost farthing; another thing at once to receive the wages of faith and courage. It is one thing, tortured by long suffering for sins, to be cleansed and long purged by fire; another to have purged all sins by suffering. It is one thing, in fine, to be in suspense till the sentence of God at the Day of Judgment; another to be at once crowned by the Lord (
Letters 51[55]:20
A.D. 253]).
Cyril of Jerusalem
Then we make mention also of those who have already fallen asleep: first, the patriarchs, prophets, apostles, and martyrs, that through their prayers and supplications God would receive our petition, next, we make mention also of the holy fathers and bishops who have already fallen asleep, and, to put it simply, of all among us who have already fallen asleep. For we believe that it will be of very great benefit to the souls of those for whom the petition is carried up, while this holy and most solemn sacrifice is laid out (
Catechetical Lectures 23:5:9
A.D. 350]).
Augustine
There is an ecclesiastical discipline, as the faithful know, when the names of the martyrs are read aloud in that place at the altar of God, where prayer is not offered for them. Prayer, however, is offered for other dead who are remembered. It is wrong to pray for a martyr, to whose prayers we ought ourselves be commended (
Sermons 159:1
A.D. 411]).
Temporal punishments are suffered by some in this life only, by some after death, by some both here and hereafter, but all of them before that last and strictest judgment. But not all who suffer temporal punishments after death will come to eternal punishments, which are to follow after that judgment (
The City of God 21:13
A.D. 419]).
That there should be some fire even after this life is not incredible, and it can be inquired into and either be discovered or left hidden whether some of the faithful may be saved, some more slowly and some more quickly in the greater or lesser degree in which they loved the good things that perish, through a certain purgatorial fire (
Handbook on Faith, Hope, and Charity l8:69
A.D. 421]).