I don't think we can identify for certain who this son of perdition was. However, we can know when he was, and most probably of whom he was - a Zealot.
Scholars generally place both letters to the assembly at Thessalonica between 50 - 51 AD.(1) Different speculations have been offered about who the man of sin was, also called the son of perdition (destruction) in the same verse at 2 Thess. 2:3, because they forget the time factor of the day of Christ in vs 2. The day of Christ was "at hand" when the letter to the Thessalonians was written. Paul was telling them that Christ was going to come in the not very distant future, or soon.
The destruction of the temple in A.D. 70 would then have been about 19 - 20 years after Paul's letter to the Thessalonians. This window of time allows for several possibilities centering around those who could have occupied, or sat in the temple during those years.
That the man of sin would be sitting in the temple, exalting himself above God means that the temple was still standing, or he could not be sitting in it. This rules out anyone after the destruction of that temple after AD 70 (CE 70).
Adam Clarke links these verses back to Isa. 1:4, benim mashchithim, children of perdition and destruction. (2)
"Ah, sinning nation, a people heavy [with] iniquity, A seed of evil doers, sons -- corrupters! They have forsaken Jehovah, They have despised the Holy One of Israel, They have gone away backward." (YLT)
A case of double fulfillment would have the sinning ones, the corrupters who turned away from God in Isaiah's day as those who repeated the same action that rejected and turned away from His Son in the first century A.D. - the Jews. So, the man of sin, son of perdition, the lawless one was one of the Jews.
The Roman emperors never ruled in that temple, and is thus another limiting factor. The one who restrains mentioned in vs.6-7 was someone Paul had already told them of, but for reasons of their safety did not name in the scriptures. It is sufficient for us to know that they knew who that person was.
That they knew who it was means that person restraining the son of perdition already existed and was already in some position of authority, otherwise he could not restrain anything or anyone.
Possibilities for that office of authority could have been the Roman governor appointed over that region - Herod Agrippa II - who tried to mediate between the Zealots and Rome to keep peace.(3) Some have claimed it was Emperor Claudius who had expelled the Jews from Rome in 50-51 AD (Acts 18:2) for causing riots over "Chrestus." (4)
The wicked son of perdition had to be someone who could have sat in that temple, and therefore had to be from within Jerusalem before the temple was destroyed. That person could only have been either one of the high priests, or one who falsely claimed to be sitting in place of the high priest. Therefore, a Jew.
Paul was reminding the Thessalonians that he had told them earlier (vs. 5), so that their questions about when Christ was coming was not the first time this subject had been raised. They knew the prophesy of the destruction of the temple (Matt. 24), and Paul was telling them again that certain things had to happen before Christ came to destroy it.
One of those things was the falling away of the new Christians back into the old law, which happened because of the constant push from the Sadducees and Pharisees. This pressure to return, or fall away would not be so prevalent, or even exist after the destruction of the temple worship system, after AD 70. Therefore again the time frame of the revealing of that Wicked one would be before Christ came to destroy that temple.
He was described as a liar and deceiver, after the workings of Satan in vs. 9 and 10. "Them that perish"... those that received not the love of the truth, and rejected the Messiah, would not be saved.... not necessarily just the Jews, but most probably centered around the unbelieving Jews who influenced any that also denied Jesus as their savior.
All of these timing factors place this man of sin, the one that exalted himself as God and opposing God to have been in Jerusalem before the destruction of that temple in AD 70. The first answer provided by Allan above offers John of Gishcala, a Zealot who was one of the leaders that fomented the rebellion against Rome in 66-67 AD. His cohort was Simon Bar-Giora.
John of Gishcala was a deceiver, one who feigned friendship with Ananas, a former high priest who had tried to get the Jews to throw off the Zealots who had captured the temple.(5) John of Gishcala then informed his cohorts inside the temple of Ananas' plans, and called upon the Idumeans (Edomites) to come to their aid in their rebellion against Roman rule.
John had been an enemy of Josephus during the time that Josephus was the Jewish general over Galilee in the first Roman-Jewish war of AD 66 -70.(6) He could very well have sat and ruled in the temple during the time before its destruction. But, there is one problem with his selection for this role of the son of perdition.
2 Thess. 2:8 says that the Lord would consume and destroy the Wicked lawless one at His coming. This would indicate that the son of perdition and destruction would in turn be destroyed, killed when Christ came to destroy the temple. That would rule out both John of Gishcala and Simon Bar-Giora, as both survived the war and were marched back to Rome under Titus' victory procession. John of Gishcala lived the rest of his live in prison.(7)
Except for what Josephus recorded, much of the secular history of this time period is lost to us, and the Bible only recorded those events that are necessary for our reconciliation to God under His plan of salvation in Christ.
Therefore, the answer to this question can only be speculation from within a certain group of people that had opportunity to act against God during a certain time period before Christ's return to destroy that temple.
All that we can say with some certainty is that the son of perdition, the lawless one was most probably that Zealot that caused the most destruction, that exalted himself as God during the occupation of the temple before its destruction.
A fair overview of the Zealot revolt of the first Roman-Jewish war can be found at That The World May Know here
Another worthwhile summary reading for the Roman-Jewish revolt and war can be found at the JewishVirtualLibrary here
Footnotes:
DatingTheNewTestament here
Adam Clarke here
2014 Telegraph here
Claudius here
Zealots Temple Siege here
Josephus & John of Gishcala, para. 13 here
Fate of the Survivors and Triumph in Rome here
