He was a fully redeemed human with no unredeemed nature to fight against - so no desires of the flesh, in my thinking at the moment.
For me; the challenge with that thinking is that it would mean Christ was not
fully human as we are and tempted in every way as we are.
That is stated in scriptures.
I do think, as have some in previous posts, that your fundamental conundrum lies in the difference between the ancient and eastern view of the ancestral/first sin (pre-Augustine/Anselm) and the western view of "original sin" which came after.
The west views the fall largely as a juridical one; where man is declared "guilty" and subject to the punishment/wrath of God.
The ancient view is different. In Orthodox thought God did not threaten Adam and Eve with punishment nor was He angered or offended by their sin; He was moved to compassion.
The expulsion from the Garden and from the Tree of Life was an act of love and not vengeance so that humanity would not "become immortal in sin". Thus began the preparation for the Incarnation of the Son of God and the solution that alone could rectify the situation: the destruction of the enemies of humanity and God, death (I Corinthians 15:26, 56), sin, corruption and the devil.
In the east, God/Christ is viewed more as the Great Physician than that of the wrathful judge. The Church is a place of healing and restoration and not a courtroom.
Orthodoxwiki article on the subject (linkage)
Something the linked article referenced which I had never considered prior; Augustine was debating Pelagianism and the condition of un-baptized infants when he first introduced the concept of Original Sin as taught in the west:
"
The fate of unbaptized infants first became the subject of sustained theological reflection in the West during the anti-Pelagian controversies of the early 5th century. St. Augustine addressed the question because Pelagius was teaching that infants could be saved without Baptism.. In countering Pelagius, Augustine was led to state that infants who die without Baptism are consigned to hell.."
The age of reason or age of accountability, as taught in the west was a result of this as well.
This is unnecessary in the east because babies are not considered guilty of Adam's sin (they are birthed into the consequences of it).