I have wondered for some time the extent to which Paul's Diaspora roots played a significant role in his psyche and theology. For example, it is easy for me to see his Pharisee days as an attempt to overcompensate for his Diaspora origins. I can also see Hellenistic Christian Jews like Stephen and Philip as really getting under his craw because of their inattention, in fact blatant disregard for Judaismos, zeal for the Law Maccabean style.
I can also see this background building up to Paul's "conversion," so called. It is what he had resisted by going to Jerusalem to be a "Hebrew of Hebrews." He could see what Hellenistic Christian Jews were saying. God was the God of all the Jews, not just the "proper" ones in Jerusalem who spoke Aramaic and were better than everyone else. In fact, God was the God of the nations too--wasn't it all there in Isaiah 56, that God's house would be a house of prayer for all the nations?
Once he affirmed Jesus as Lord, the things that had gnawed at him snapped into place. The good news must be preached to all Jews and all the nations.
It is at this point that the relevance of Philo really kicks in. Philo valued his literal Jewish heritage. He had pride in the temple and gloats in the demise of Caligula, considering it appropriate to someone who messes with God's stuff. "It is not so easy to counterfeit the form of God" (Embassy)
Philo considers the Roman governor Petronius very wise for not following through with Caligula's order to put his statue in the temple precincts: the Jews "would willingly die not once but 10,000 times than see something done that was prohibited... Their diligence about the temple is more intense and distinctive than all of them" (Embassy 209, 212).
However, these sorts of comments are personal and political. Philo did not actually believe that the temple was necessary for atonement. The true temple of God is the universe, which the physical temple symbolizes. A human couldn't build a house to contain God (Cherubim 99). You could use the physical temple to indicate your thanks or to ask forgiveness. But it was not necessary for this (Special Laws 1.67).
What is important is the attitude of one's heart. A hundred bulls a day would not suffice for forgiveness if one's intent was wrong (Planting 108; cf. Moses 2.107-8). "But He receives those of blameless intent, even if they sacrifice nothing at all. God takes delight in altars without fire, where the virtues play the role of the choir" (Planting 108). Those whose minds are set on virtue are in a holy place even if their bodies are not (Allegorical Laws 1.62).
My suspicion is that while Diaspora Jews on the whole valued the Jerusalem temple, literal sacrifices may not have played a large role in their religious life. They sent their yearly offering, perhaps dreamed of one day making a pilgrimage to see it. The valued it and were deeply stirred by Caligula. But it is easy to see where they might not be zealous for it as a means of atonement. After all, the temple at the time was constructed by Herod the Great--not a hero of Jewish faith. And it had some associations with the Roman administration of Judea.
In short, there is nothing particularly startling about Paul's spiritualizing use of temple and cultic symbolism, and in itself it says nothing of certainty about his attitude toward the Jerusalem temple. He seems to assume the legitimacy of the temple's operation in 1 Corinthians 9:13. At least he doesn't question it. And 2 Thessalonians 2:4 seems to imply condemnation of a man of lawlessness setting himself up in the temple as God.
The greatest objection to Paul having a place for the temple in his theology is his teaching on justification by faith and the accompanying defeat of the power of Sin by the Spirit. What sins would there be for the temple to cleanse thereafter? We immediately see why the temple plays virtually no role in Paul's theology--and why one of his heirs, the author of Hebrews, could see Christ as the complete reality behind it.
We should also note that Paul probably shared Stephen's sense of the temple as off track. After all, he had apparently worked for the high priest. Then there are unintentional sins and the role of the temple in those intentional sins that one does commit, not to mention offerings of thanksgiving and praise.
So Philo's sense that the heart was what mattered, even in sacrifice, seems similar to Paul's sense that we have a spiritual worship and that the church offers its body as a living sacrifice. The temple was tangential to Paul's theology, but it did not clearly contradict it.