The temptation to power may have been simple reconnaissance, but the suicide dare from Mount Zion seems a bit extreme from all angles. Had the devil somehow anticipated - in his own simplistic and perverse way - that God would later have Jesus die and return to live, as a witness to Israel? Probably not, or not quite. Still, the rocks-to-food bit was a 'prove it to me' kind of dare. This suicide bit was a 'prove it to Israel' dare.
From Jesus' response to the suicide dare, the devil may have surmised that Jesus seemed particularly disinterested in proving himself to Israel. Knowing the long history of God's involvement with them, Satan may then have leaped to suppose God's new plan for this 'Son of Man' was to expand his foothold on the Earth. Although anciently God declared himself pleased to hold Israel, originally, Satan knew God had claimed all the world, and given it to Man. (On the question of "Adam", see post #3.)
Now faced with a divine one who stood as a man, Satan must have thought twisted thoughts. We'd be ill advised to try reconstructing those thoughts (for a number of reasons!) and unlikely to succeed (at any rate), but what that process evidently came to, for Satan, was a very odd conclusion that this Jewish Divine Man might very well be interested in accepting the reigns of earthly dominion. (Whether the offer was valid or not is irrelevant to Satan's apparent hope that Jesus might say yes.)
The peculiar nature of all this may even have struck Jesus as odd. We don't know if the Father had yet brought Jesus to anticipate that he'd inherit all things, that he was meant to become "King of Kings", that he'd die and be resurrected, or - even - that he'd be transmogrifying bread, fish and wine, in as soon as a few months. We don't know if Jesus had imagined himself doing these things. (John's commentary on Cana at least strongly suggests that he'd not done such things before now.)
What we're told is that Satan suggested these things. The question is, was Satan the first one suggesting these things to Jesus? In some ways, not at all, because certainly Jesus had heard the miraculous stories from scripture. Stones to bread was as reminiscent of manna as it was a new trick. Resurrection was performed once or twice in the presence of prophets.
In another way, though, Satan must have been first. Unless some human being had actually said to Jesus, You can do such-and-such, and even if the Father had somehow hinted, or Jesus had somehow imagined, there would still have been a fresh, startling quality to the devil's suggestions. Make stones into bread? Jesus' response was exemplary, but in some part of his mind, he must have been wondering, could I? More likely, perhaps, he was praying, Father, can I do that?
Side Point: the stark freshness of Satan's words may have caused Jesus to remember them extra vividly. As with all notable quotes, especially considering more than half of what got recorded came from Deuteronomy, the memory of a powerful one liner is more accurately reported, and should be judged as more credible, than long speeches, which ancient historians normally reconstructed from various sources.
Please note, I do not mention this freshness as a way of concocting support for the story's veracity. Far more compelling, to me, is this realization that Jesus was probably somewhat startled by these three temptations.
The last one, however, exceeded his tolerance.
To be concluded...