This is sort of a combination and customization of several commentaries I perused on the subject, being curious myself. As I am not directly copying any one of them I am not adding individual quotes. The two that most influenced my opinion here is Edersheim and someone called Arthur Sloman.
If you read the verses carefully you will notice Luke does not imply chronology as much as Matthew. Matthew uses the word 'then' a couple times. Luke just uses the word 'and' (i.e. this also happened among these things). At once we should see that the gospel narratives did not have an obsession with chronology as we might have in a modern account. Those who spend years trying to chart the 'true' chronology of the gospel events have various perplexing decisions to make and leave many things under guesswork.
To wonder why Luke may have reversed the potential chronological order of Matthew's account we can only make an educated guess. The 'education' part in a good guess is that we do know that Luke was thinking more of a Gentile audience whereas Matthew was minding a Jewish audience. This is often the only handle we have to try and see why one goes in a certain direction and the other not.
Using this handle of the intended audience I can see one plausible explanation. For a Jewish audience they might instinctively understand that the temptation to 'throw himself down' or to become like a powerful Lord of the earth, are both increasing degrees of the same temptation to obtain a Messianic dream the easy way. That is to prove or force his kingdom without suffering or being rejected by his people. To a Gentile, this order of increasing temptation might go right over their heads. Without digressing and explanation the whole context, possibly Luke was satisfied in getting a less 'deep' understanding of the temptation that might be more applicable to a Gentile audience and their temptations. The First the temptation is just to satisfy hunger, without any direct religious significance in the desire. The Second is then to a Gentile application, to satisfy a desire for raw power (neglecting the Messianic motive to have that power and fulfill the Jewish expectation of the Messiah's rule according the the flesh). Finally to satisfy a desire for renown recognition and fame, which seems the ultimate dream of stardom like the gods of Greece and Rome we find the grand temptation (again avoiding the complexity of the Messianic nuances of the chronological order). Maybe Luke switched the order of these temptations so as to better connect and apply more aptly the gist of the narrative to a heathen audience entirely ignorant of the Messianic nuances that the chronological order introduces. If he used a chronological order he may have had to embark on some digression and side notes of explanation cluttering his evangelical intentions.