Was Jesus impeccable?

i) It's intuitively appealing to say that temptation requires an ability to succumb to temptation. But we could turn that around. Temptation is most unbearable when the opportunity presents itself, but you know that you cannot give in. 

Suppose my kid brother and I live in West Berlin c. 1961. We're both teenagers. We make a short trip to East Berlin. But that's when the Russians close the border. So we're trapped in East Berlin. We're cut off from the rest of our friends and family.

Suppose I have an opportunity to bribe a guard at Checkpoint Charlie. He'll let me escape, but not my brother. I'd never see him again. 

It's very tempting for me to return to W. Berlin. I desperately want to return. Yet it's utterly unthinkable that I'd abandon my brother. In that case, what makes the temptation so galling is that I have the opportunity to do so, but as a practical matter, I have no real choice. Morally and psychologically, I could never bring myself to betray my kid brother.

Compare that to say, sexual temptation where there's no sense of moral restraint. That's temptation without resistance. Cheap temptation. 

ii) Unless one believes that the saints in heaven can still commit apostasy, a capacity to sin is not intrinsic to human nature.

iii) Unless the human nature/will can operate independent of the divine nature/will, Jesus cannot succumb to temptation. 

iv) Incidentally, that would make for a perpetually unstable Jesus. After all, he still exists! The Incarnation is permanent. He will live in that state forever.

So it isn't just a question about could he sin during his 33 years (give or take) life on earth, 2000 years ago. If he has the capacity to give into temptation, then that's a constant possibility.