If it is possible that the Lord Jesus Christ could have yielded or been deceived by sin, then one must also conclude that it is possible for him to have given inaccurate information about eternal things when he was growing in wisdom and stature and favor with God and man.
So the question becomes: we know Jesus did not sin but could he have sinned in order to have experienced temptation as we do? Was Jesus capable of sinning? while we think of temptation as "the possibility of sin." we want to say as human beings, "temptation implies the possibility of sin. If a person has no susceptibility to sin or if sin has no appeal for him, the temptation is a farce. Some will argue this point.
To understand Hebrews 4:15 we need to understand what "temptation" means.
The Greek word to "tempt" does not mean to induce evil. the word means 'to try, to make a trial of, put to the test... it means to signify the trying intentionally with the purpose of discovering either good or evil. The power or weakness was in the person or thing.
Therefore Christ faced real challenges in the desert where he proved the good that was in him. In the desert Christ was faced with the enticement of a person (Satan) to commit sin by offering some seeming enticement... power, wealth or food.
Jesus was God and possessed the attributes of God. There was nothing that Jesus could be enticed to have or obtain, just as Satan was unable to entice Jesus.
Yet in the temptation of Satan, Jesus was asked to do the things he could do and the things he wanted; the results of which would have come from doing what Satan asked.
The nature of his temptation was..the fact that he as God was tempted to do the things he could do. the things Christ was asked to do...appear to be valid requests.
Therefore, because Satan asked Christ to do the things he was capable of, e.g., turning stones to bread, etc, we can see that the temptations Christ faced were real.
The temptations of Jesus were different from those that we face. "Jesus was tried as no other was ever tried. He faced the temptation in the garden of Gethsemane to abandon the plan of God and to "let this cup pass from me." Matthew 26:39.
So Jesus in reality experienced worse temptations than we do. the temptations of Jesus were real for sure, because they were tests of and trials of his power.
So when the Bible says Jesus was tempted, it implies he was tempted in al his thinking, desires (emotions) and decision-making ability.
Christ was tempted in every part of his being as a person is tempted in every part of human nature.
One other point here is that one can be tempted to sin in an area that he is not necessarily susceptible to sin. I can be tempted by tv ads to drink beer and I am not at all susceptible to drinking the beer. While I am daily attacked, I cannot be conquered in this area.
One theologian said this "while the temptation may be real, there may be infinite power to resist that temptation, and if the power is infinite, the person is impeccable"
We thus say, that the argument that Jesus was tempted does not support peccability. As we said, for one to be tempted does not necessarily imply that one must be susceptible to the temptation. Yes Jesus was tempted, which does not imply that he was tempted to watch beer ads on tv, nevertheless what he did experience was real temptation.
And just because Jesus was tempted does not imply at all, that he was capable of sin. It is possible for Satan to do the impossible, i.e. tempt Jesus, even though there was no chance of success; and Satan knew it too.