I think Jesus took on a humanity of being as much as he could be tempted. Why would Satan bother, otherwise?
True. But even a human being with an un-fallen nature --- I'm thinking, Adam and Eve in Paradise before the Fall --- could be tempted.
So let me re-phrase the question: do you think Jesus' human nature was that of Adam and Eve in Paradise before the Fall, in other words, pure and perfect in a creaturely sense --or-- did He have, like the rest of us, a degraded human nature as a result of the inherited consequences of sin, which darkened the human intellect, weakened our will, and deranged our appetites?