To the best of our knowledge, medieval monks and nuns were, well, religiously scrupulous about making exact copies--right down to replicating obvious errors in their exemplars and sometimes even copying the exemplar's date or scribal colophon (name of the scribe who had made the previous copy), if the manuscript in question had one.

But while they faithfully preserved classical texts with their basic chronology of events, Christian original authors (starting already in the early Church, long before Constantine) cast a Christian sheen over the past and present that brought Roman actions, persons, and literature into a Christianized history and future.

Probably best known is the era of persecutions under pagan Roman emperors seen to start in Acts of the Apostles and continue down to Constantine. While there were periods and localities of danger (our earliest Christian autobiography by a woman, the Passio Perpetuae, recounts her experiences leading up to her execution in the gladiatorial arena), these were by no means constant or imperial, as ongoing scholarship continues to show. Even while creating the mythology of an Age of Martyrs, early Christian writers agreed. Eusebius of Caesarea infamously blames the emperor Severus for the persecutions that led to the deaths of Perpetua and Felicitas, but Tertullian of Ridiculously Convoluted Latin credits him with tolerance and even helping protect Christians against the violence of pagans.

Beyond the mythology of a Church incubated in blood, medieval Christian writers worked to Christianize, after a fashion, the Roman leaders and texts that they admired and needed a way to justify that admiration. No, they did not go back and say "Trajan was Christian." However, that emperor was seen as a virtuous hero, and medieval theologians worked to justify his placement in limbo at the very least.

So medieval women visionaries, who were believed to have a direct line of sight to the levels of the afterlife, always disambiguate wildly and very cleverly when asked questions about whether Trajan is in heaven or hell. They couldn't say yes...but they couldn't say no. (And yes, visionaries did field questions about him--his defense of Christians was considered a big deal). Dante and Aquinas are unambiguous: they follow the legend that early medieval pope Gregory the Great prayed Trajan's soul back to life for conversion so that he would then go to heaven.

Classical literature also found its way to Christianization. Ovid--batty, sexy, polytheistic Ovid--and his Metamorphoses were disseminated as the Ovid moralisee--allegorically interpreted, in the same way the Bible way, for their claimed deeper, true moral meaning. (It's impressive.) The Sybilline oracles, too, were recast as predicting the birth of Jesus and occasionally other events in Christian history.

You might say, in the end, that the preservation of classical texts in and of themselves, and the recasting of their characters and stories as Christian in new texts, were part of the same continuum. Medieval Christianity nurtured a deep respect and love for Greece and Rome, and worked to justify that admiration of a pagan world in an age of Christian faith.