The temple was destroyed sometime around AD 70.
Which New Testament books were written after that catastrophe?
Do these books comment at all on the destruction of the temple?
The dating of the New Testament is a matter of some controversy, so there is no consensus answer to the question of which ones were written after the destruction of the temple. (The Old Testament books were of course written well before).
No New testament documents make clear reference to the destruction of the temple. Some appear to prophecy the destruction, but it is clearly written as prophecy and not fulfilment, and even then it is not an absolute certainty. Many scholars use this information to date the NT canon as fixed before the destruction of the temple, on the reasonable grounds that had it been known about some NT writers would certainly have mentioned it as evidence of the correctness of prophecy. Bishop John A Robinson makes a well-argued case for this in his book "Redating the New Testament", or its popular version "Can we Trust the New Testament?".
Extensive quotes of the New Testament in letters known to be written at the end of the 1st century AD show that the NT documents were well known and accepted by that time, although it is technically possible that they may have undergone further editing between then and the dates of the first positively dated manuscripts from a hundred years later.
So to answer the questions:
Raymond E. Brown says in An Introduction to the New Testament, page 164, there is wide scholarly agreement that Mark's Gospel was written in the late 60s or just after 70, and therefore the destruction of the temple was imminent or had already occurred. Burton L. Mack goes as far as to say, in Who Wrote the New Testament, page 152, it would not have made sense before the war had run its course and the tragic fate of the city was known. The prophecies in Mark chapter 13 are clearly of the First Roman-Jewish War and of the civil war that raged concurrently within the Jerusalem walls, but these prophecies were written with after the event. Had Jesus prophesied the destruction of the temple, he would have been correct, but this prophecy was followed by another prophecy that he would return on clouds of glory within the lifetimes of those to whom he spoke, an event that did not occur as prophesied. Since it is not possible for Jesus to make a prophecy that does not come true, these were not his prophecies and were actually written at the end of the War.
Most scholars now believe that Matthew and Luke were substantially derived from Mark's Gospel. In fact, John Dominic Crossan, in The Birth of Christianity, page 110-111, speaks of a massive consensus among scholars in favour of Markan priority. On this information we can say that the Gospels of Matthew and Luke, being written some time later than Mark, were certainly written after 70 CE. Acts of the Apostles was written some time after Luke, although it does not mention the destruction of the temple nor the Roman-Jewish War of 66-70.
John's Gospel is generally dated 80-110 CE, although critical scholars, who see it as influenced by Luke's Gospel, would place in towards the later end of this range. The three Johannine epistles were written shortly after the Gospel.
Thirteen epistles have been attributed to the apostle Paul: Romans, 1 Corinthians, 2 Corinthians, Philemon, Galatians, Philippians and 1 Thessalonians, but five of these are regarded as disputed. Paul's genuine epistles were, of course, written before 70 CE. Known to critical scholars as pseudo-Pauline epistles, Ephesians, Colossians, 2 Thessalonians, 1 Timothy, 2 Timothy and Titus are thought to have been written between 70 Ce and the first half of the second century.
Critical scholars place the First Epistle of Peter no earlier than 80 CE, and the Epistle of Jude and the Second Epistle of Peter in the first half of the second century. Jude, perhaps carelessly, self-identifies as written long after the apostolic era, while scholars have noted that 2 Peter uses material from the earlier Epistle of Jude.
The Book of Revelation is almost universally accepted as having been written after 70 CE.