You say in your answer, “By definition a temptation has to be desirable to the person being tempted.” Is it not also a desire to do something that we know is wrong? I understand that when we are being tempted we have a desire in our heart to sin in some way.
I understand from the verses on anger and lust that our hearts can sin even if we don’t act on it and the temptation to sin begins with our heart’s evil desire. With that in mind I too don’t understand how Jesus was tempted in all ways-just as we are and yet was without sin? (Hebrews 4:15)
If Jesus was fully human then He was subject to human emotions. Since the Bible said in one place that he was tempted by Satan (Matt. 4:1) and in another that He was tempted in every way (Hebr. 4:15) then it’s safe to assume this was the case. There would be no reason for the Lord to exaggerate this or mislead us.
Temptation is an enticement to sin. We have the choice to respond or not. Therefore the sin occurs when one considers yielding to temptation, not when the temptation is actually presented. Looking at a woman isn’t what causes a man to sin. He sins by consciously forming lustful thoughts about her.
As I said in my answer the absence of a sin nature only helped the Lord to resist yielding to the temptation. It didn’t render Him immune. After Jesus had fasted for 40 days he was hungry. Satan reminded Him that He had the power to turn rocks into bread. He knew that doing so would exceed the parameters of His mission, which was to live the life of an ordinary man, so He refused to even consider yielding to the temptation. By refusing He avoided sinning.