Up high, to the "pinnacle" of the Temple? IF "pinnacle" was in Mt.4:5 or Lk.4:9, I might believe it. How else could the two of them even get to the roof!?! But "pinnacle" is not in these scriptures. Therefore, I don't find it necessary to conclude either Satan or Jesus ever stood on Jerusalem's roof. But then, what did they do?
Early English translators, perhaps playing to the high drama in the passage, transliterated the Vulgate ("pinnaculum") in rendering πτερύγιον as "pinnacle". The Liddell & Scott Lexicon suggests this, however, for pterugion: "in a building, turret or battlement, or (as others) pointed roof, peak, Ev.Luc.4.9". Now, let's bookmark 'turret or battlement' for a moment so I can fuss about 'Ev.Luc'.
I don't like when L&S cite obscure NT usage to illustrate supposedly unique meanings, especially when it appears they're trying to apologize for a conventional translation. (See here and here for more examples.) I suppose we might say that Jerusalem's (so far as we know) flat-roofed Temple could still have a "pinnacle", but it had no "point" or "peak", so what are L&S playing at? By the way, when Jerome wrote the Vulgate, circa 400 AD, virtually all temples DID had pointy roofs. Thus, pinnaculum? I'll bet that was part of it.
Regardless of roof shape, L&S did their other work well. The root of 'pterugion' meant the wing of a bird or the fins of a fish (including dorsal along with the side fins, apparently). In humans, it could refer to the shoulder blade. So - Vulgate aside - while it looks like 'pterugion' could refer to the top of Jerusalem's Temple, it seems more likely to imagine two people gaining access to and then standing atop the side parapets, the defensive positions around inner and outer courts, or perhaps even the Fortress Antonia, adjoining the Temple's north side, with its commanding view of the city and Temple courts, both.
Both Matthew & Luke use the phrase πτερύγιον τοῦ ἱεροῦ, the last word of which refers to the Temple precincts as well as the sanctuary. Thus, if these dramatic accounts of Satan leading/taking* the Lord up to Mount Zion is to be taken as an actual historical event, we do not have to imagine they 'beamed' their way to an otherwise unreachable height. To the contrary, all that reason demands of this passage is to suppose that Jesus walked up to the Temple, and got up on one of the much more easily accessible positions.
Next: Did the Devil give Jesus a vision from way up high?
* [Update: Matthew uses παραλαμβάνω as "take" twice in this passage, as well as 14 other times, 12 of which are clearly for physical travel. The other two (24:40,41) are thought by some to refer to the rapture, but that interpretation is extremely doubtful.