Did Jesus visit the temple before the wise men came?

I was looking into the accounts of Jesus' birth both in Matthew and Luke and tried to make something of a chronology of the events on a piece of paper so that I can get it clear in my head. The thing that I came to notice is that there could be a large time gap in between Luke 2:38 and Luke 2:39... Now if we read the 2 accounts carefully we will understand that the wise men came to Jerusalem (The city of the King), expecting to find the newborn King there. However, Herod, consulting the scholars of the day sent them to Bethlehem (as it has been prophesied) (Mat. 2:1-6). Now, we are not actually told that they actually went to Bethlehem as the star appeared and guided them again. However, certainly that is the assumption of most people. Later we read (Mat. 2:16-18) that Herod went about killing all the male children aged 2 years or less, based on the information he had acquired from the wise men, concerning the time that the star appeared (Mat. 2:7). So it is safe to say that the wise men came to Jesus anytime before He was 2 years of age. However, what makes it more interesting is that it is written that after the wise men left, Joseph was told in a dream to flee to Egypt with Mary and Jesus. Knowing this, we look back into the account by Luke and see that they went into the Temple in Jerusalem, for the cleansing of Mary (Luke 2:22) as it is written in the Law (Lev. 12:3-8)... According to this passage for a male child this is done 33 days after (birth?). Which would mean that they visited the temple before the wise men came to them? And then returned to Bethlehem where the wise men came (even though Lk. 2:39 says they went back to Nazareth - assuming there is a gap and this speaks after their return from Egypt.) **OR** they went back to Nazareth straight after the cleansing in the temple (approx. a little over a month after the birth), meaning that even though the wise men were sent to Bethlehem by Herod, the star guided them to Nazareth..? **So, my question:** Now, more than one question arise from the comments above, however my main question is: According to my observations, is it safe to say that Jesus went to Jerusalem and into the Temple before the wise men got there? Are there other places in Scripture that confirm this or is there perhaps a flaw in my logic?