“While he lived on earth, anticipating death, Jesus cried out in pain and wept in sorrow as he offered up priestly prayers to God.” [Hebrews 5:7-10 The Message ]
Christians – and knowledgeable nonChristians tend to restrict Jesus' feelings to religious contexts. The preceding verse his feelings are exhibited while in prayer – which puts us in mind of His prayers in the Garden of Gethsemane.
However there is no indication that Jesus Christ's feelings were restricted to prayer alone (prayer and feelings is an interesting topic in itself). In fact, it is quite the opposite. From the gospels we know Jesus exhibited anger, pity and sorrow. All these have legitimacy as good religious feelings, as long as anger can be labeled as “righteous” anger.
Let’s not forget Jesus did have a friend he felt (feelings) especially close to: the disciple "Jesus loved" (left unidentified but mostly thought of as John). And, then there is Lazarus, who though not an apostle, was deeply loved by Jesus.
Evidently Jesus did have personal preferences: we find he felt connected with some people more deeply than others and this connection doesn’t seem to be a one-to-one relationship with their stature as spiritual giants. It had more to do with a personality preference, and another feeling called friendship.
Let's also remember that in addition to the "religious feelings" listed (righteous anger, pity, sorrow) and friendship, that Jesus felt weak and wobbly-which is my 21st century term for the biblical word "tempted." Of course, we are tempted every day, usually many times a day, if not all day by many things. We are tempted to conceit, fear, anxiety, despair, discouragement, helplessness and hopelessness, mostly unbelief. We are also driven to participate in "sins of the flesh" (those normally associated as bad: greed, lust, power, etc.).
"...we do not have a High Priest who cannot sympathize with our weaknesses, but was in all points tempted as we are, yet without sin. Let us therefore come boldly to the throne of grace, that we may obtain mercy and find grace to help in time of need." [Hebrews 4:14-16 New King James Version]
Scripture declares Jesus was God come in the form of flesh-a man...and our feelings is one of the many good reasons He had to come as a man.
Were Christ untempted, then He would be unfeeling as a human. Praying to a god who was unfeeling as a human, would be like asking an unseeing god to restore your vision. You see, he wouldn't understand the quality of your lack of vision, and therefore its need. Nor would such a god make you feel at all encouraged that he could understand your desire to have vision restored.
Now, on the other hand, had Christ been tempted and sinned, He could not be a savior, nor could he qualify as a High Priest to make intercession to the Father on our behalf.
"God could, had He pleased, have been made incarnate in a man of iron nerves, the Stoic sort who lets no sigh escape him. Of His great humility He chose to be incarnate in a man of...sensibilities who wept at the grave of Lazarus and sweated blood at Gethsemane. [If this had not been the case]...we [might] have missed the great lesson that it is by his will alone that a man is good or bad, and that feelings are not, in themselves, of any importance.
...knowing that He has faced all that the weakest of us face, has shared not only the strength of our nature but every weakness of it except sin. If He had been incarnate in a man of immense natural courage, that would have been for many of us almost the same as His not being incarnate at all."
- C.S. Lewis, Letters to Malcolm