Temptation implies possibility of sin in general (humans) but not in specific (Christ). For instance, the testing of gold implies the possibility of things not being gold in general, but not the possibility of pure gold not being pure gold. The end of testing gold is to distinguish true gold from false gold. Thus, Christ's not falling in sin proves He could not sin. Since, Jesus is God and sin is rebellion against God, Jesus could not sin, for it is impossible for Him to rebel against Himself, unless His omniscience and omnipotence were brought into question. Thus, being human, He was tempted, but being divine and undivided in His moral nature, He was essentially holy and so could not sin.
Jesus is one Person. That person cannot sin, because divinity is sinless, and Jesus has a divine nature. Nor is it proper to say that Jesus "might have been able to sin in his human nature," because persons Will (or Act); natures Are.
Two wills implies two natures. Again, Persons ACT. Natures ARE. There is nothing strange about two wills acting in harmony. Your will and my will can be two wills acting in harmony. If your will is subservient to my will, or is guided by my will, that doesn't make it any less your will. The unique thing about Jesus is that it was one Person having two wills, each according to its nature: one human, the other divine.
For a temptation to be "real" it should be sufficient that it has an apparent advantage or attraction. So, for example, Satan suggests to Jesus the opportunity to "inherit the world" but in a way that avoids the very real agonies of the cross. How could this not have obvious attraction? In other words, how could this not be an actual temptation?
If it be objected that Jesus knew there was a better (best) option available by obedience to God, therefore no other options held any attraction, I respond that this view does not give due weight to the full human nature possessed by Jesus. The same objection could have been raised to Adam's sin. The same objection can be raised to the Christian's sin today. And even (to a much less degree) to the unregenerate in those cases where the "right" thing is plain and obvious, but people still choose the sinful option over one better.
No one who falls to temptation ever knows its "full" weight. Only those people who successfully resist a temptation know that temptation's full power. For they have exhausted its strength, and resisted. Jesus NEVER lost a battle.
As the many discussions of hypotheticals in the debates showed, you have to define impossibility as relates to Jesus and temptation. But here's the simple fact. It was decretally impossible for Christ to sin, for God had from all eternity decreed that He would not sin. The fact that Jesus did not sin establishes the preceding decree that He would not sin.
So questions about the intrinsic peccability or impeccability of Christ's human nature are all firmly committed into the realm of the theoretical. While they can be discussed in that realm, I think it should be kept in mind that it is only as a counterfactual hypothetical that they even arise; not only because Christ did never actually sin, but also because it was infallibly foreordained that He never would.
If we may aver that the elect angels will never sin, as did those who did not keep their first estate, and thus they are by God's decree unable to sin, we must further observe that their inability to sin is not intrinsic. It is God who sovereignly keeps them.
Christ however, is intrinsically unable to sin. Satan approaches to tempt but has nothing in Him (John 14:30). The Man Christ Jesus not only came forth from the womb sinless but He came forth from the womb as the Theanthropos. Jesus, the Person, having both divine and human natures, cannot personally sin.
Even the redeemed in glory will then be non posse peccare, will be so not by intrinsic power but by the will and power of God. With the God-man it is otherwise. He is self constitutionally unable to sin; He is God.
AMR