Interesting question. Lets start with the word used for tempted first.
In Greek:
peirazō
1) to try whether a thing can be done
a) to attempt, endeavour
2) to try, make trial of, test: for the purpose of ascertaining his quality, or what he thinks, or how he will behave himself
a) in a good sense
b) in a bad sense, to test one maliciously, craftily to put to the proof his feelings or judgments
c) to try or test one's faith, virtue, character, by enticement to sin
1) to solicit to sin, to tempt
a) of the temptations of the devil
d) after the OT usage
1) of God: to inflict evils upon one in order to prove his character and the steadfastness of his faith
2) men are said to tempt God by exhibitions of distrust, as though they wished to try whether he is not justly distrusted
3) by impious or wicked conduct to test God's justice and patience, and to challenge him, as it were to give proof of his perfections.
We can see that the meaning isn't strictly defined to the way we view the word temptation in English. It is also a testing, an attempting, a trying of one's faith, or even simply a solicitation of sin by the devil.
I think when we think of temptation, we view it in the light of our fallen nature where we have a propensity to sin. Where the sin to us actually seems appealing, because it speaks from the fallen nature of the devil to our own fallen nature. The sin is solicited to us by the devil (or I should say one of his servants) and it strikes a chord with our own sinful nature, to the point where we entertain the appeal of it.
But we notice how crafty the devil is. He doesn't usually solicit something beyond what a person is prone to give in to.
For example, if I were to come up to you on the street, and say, "Hey, proudpapa! What would you say to a fun-filled evening of robbery, cocaine use, murder, and rape? I'll provide all the means! Are you in?"
I would venture to say that you would find the idea utterly repulsive. Even though the "temptation" is there, it would not appeal to anything in your nature (especially being redeemed) and would in fact be unthinkable. I would be tempting you, but it would probably hold no sway.
Now the devil knows this, thus, it's not the angle he uses. For us, he'll say things like, "Take another look at her." "Exaggerate your position of importance JUST A LITTLE." "Take personal offense at that remark." "Look how much deeper your knowledge and walk is than THAT brother over there." etc. etc. Because this takes advantage of the sin still in our lives that we struggle with.
Now we get to Christ. Not born with a sinful nature like the rest of mankind (I know you've debated this point before, so we'll just leave it at that)so the sin itself, when presented, does not entice Him to go beyond the command received by His Father. It's not a sinful appeal appealing to a sinful nature. It's a sinful appeal to One who knows no sin.
Now He still could have said yes, the way Adam and Eve said yes, but just the fact that the sin was presented to Him, should not be mistaken for the way we take in temptation some of the time. Where we mull over it, and fantasize about what would happen if we were to sin, etc. etc. Remember that Adam and Eve still had no sin until they actually ate of the fruit.
And Eve was deceived. Who could deceive Christ?
James 1:13-15 is pretty good in light of this as well I'd say.
Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man: But every man is tempted, when he is drawn away of his own lust, and enticed. Then when lust hath conceived, it bringeth forth sin: and sin, when it is finished, bringeth forth death.
And coupled with Hebrews 4:15;
For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yet without sin.
And 2 Peter 1:4;
For by these He has granted to us His precious and magnificent promises, so that by them you may become partakers of the divine nature, having escaped the corruption that is in the world by lust.
In the new divine nature we've received, we now have the ability like Christ, to be tempted, yet be unswayed. As the devil's sins will not appeal to the divine nature. Only the flesh.
Just my thoughts on the matter.