IF the story is factual, it requires reconstruction. Leaving the story untouched creates more doubt than a sympathetically critical reassessment. Such things should be presented conditionally. IF these purported events were part of Jesus' actual experience, then how must they have transpired, four dimensionally?
The narrative as is cannot fully contain its own content. Matthew says the fast was over when Satan tempted Jesus about eating. Jesus must have walked to Jerusalem, and could never have stood on the "pinnacle" of the Temple. Any mountain between Jerusalem and Nazareth would be a suitably dramatic site for the devil's mysterious projection show, but Matthew's emphasis on height can't have had anything practical to do with it.
Mark's synopsis is chronologically dubious, condensing everything to 21 words in Greek. The syntax may suggest a progression, but the geography is unclear. If the second clause corresponds with the first clause, then the devil was also testing Jesus during his fasting experience. But does that mean tempting? Or taking his measure in preparation for the three temptations to follow? And when do Mark's angels minister to Jesus? During the fast? Or after the temptations? If the latter, then when were the wild beasts? Keeping wild beasts in the trandjordan probably means Satan tempted (or 'tested') Jesus BOTH during AND after the 40 day fast; and Mark's angels may have come down at any point.
All things considered, if the devil is real, and if Jesus found these brief exchanges startling enough to remember, and reported them accurately to someone who wrote them down - then - it is plausible enough to reconstruct the historical picture of what must have happened. My own fledgling attempt just posted: Part 1, Part 2, Part 3, Part 4 & Part 5.
Preliminary reasonings had also been posted, beginning in June: Allison on Jesus' Wilderness Temptations, Did Jesus really debate Satan?, Did Satan teleport Jesus?, Situating Jesus' Diabolic World Vision, Sequencing Jesus' Temptations, Situating Jesus' Temptations.
In the end, no one has to believe these things transpired. But IF we believe they transpired, and yet we make no attempt to work out HOW they transpired, then - to the ears of many of our listeners, and perhaps to our own selves - we may as well be declaring them not-to-have-happened. That is, if we forcibly keep scriptural stories only within the realm of literature, then we tacitly label them fictional literature. The content of non-fiction literature, of its course, must eventually come into, and be held up against, the concrete faculties which make up 'the real world'.
Believe that a man walked on water. Or not. I'd be willing to suppose that the devil 'beamed' Jesus to the Temple's roof. But the scripture does not say that. What it does say must be matched with the real world. That is, IF, we intend to declare it as real.