Is purgatory mentioned in the New Testament and has Jesus taught about it in his sermons?

Purgatory is the name given to the final purification of the elect (CCC 1030 – 1032). Though the doctrine is not mentioned explicitly in Scripture, it is present in the teachings of Jesus and his apostles. One such example would be Luke 12:43-48 where we find Jesus speaking about a returning master and four different types of slaves. The return of the master (Jesus) points towards the impending judgement that awaits each one of us where we find out whether we will enter into the kingdom of God (master’s household) or not. So, what happens when the master returns? If the master finds his slave at work (being faithful and obedient), he will be put in charge of the master’s possessions (enters the household of God, heaven). If the same slave is found to “to beat the other slaves, men and women, and to eat and drink and get drunk”, he will be cut into pieces (a permanent state) and put with the unfaithful. I.e. he will be cast out of God’s kingdom “into the outer darkness, where there will be weeping and gnashing of teeth” (Mat 25:30), hell.

If there was only heaven and hell, Jesus would have stopped here. But we find him going on to talk about two more types of slaves. The third kind of slave “knew what his master wanted, but did not prepare himself or do what was wanted”. As for the fourth slave, he “did not know and did what deserved a beating”. It should be noted that both the third and the fourth did not abuse others (beat other slaves) or abuse himself (get drunk) like the second one but where just not ready for the master’s return. Both of them receive a severe and a light beating correspondingly, a temporary punishment, but in the end, they are not cast out of the master’s household.  

This forms the foundation for the Church’s teaching that at the time of judgement, there would be some whose sins are not grave enough to be sent to hell nor would they be pure to enter into heaven. These souls will have to experience temporal punishment and be purified before entering into God’s glory. This process of purification is called purgatory. The same can be found in the teachings of St. Paul (1 Corinthians 3:15) where he talks about a builder (the soul) suffering loss (temporal punishment) when his work is tested with fire (purification process) but in the end who gets saved (enters the kingdom of heaven).