No. This is the paradox presented by traditional understanding. That Jesus* could be fully human and fully God. The scriptures show no such conundrum, but express Jesus as the 'form' or 'image' of God. Thus requiring him to not be 'infinite' as you suggest it must imply.
There is nothing 'infinite' in a man who could die. There is nothing 'fully God' in a man who can be tempted, or potentially sin as Jesus' prayer in Heb 5:7 demonstrates.
During the days of Jesus' life on earth, he offered up prayers and petitions with fervent cries and tears to the one who could save him from death, and he was heard because of his reverent submission.
There is nothing in the text describing Jesus somehow stopping having the attributes of God. How can God not be God? Jesus is either God or he is not.
Jesus' own words were that he was a man John 8:40
As it is, you are looking for a way to kill me, a man who has told you the truth that I heard from God. Abraham did not do such things.
If we choose to make him also God, this is not of the text. (why is Jesus, allegedly God, receiving truth from God?)
There are simply too many strange paradoxes created by making up things the bible never speaks of. How can Jesus rely totally on the Father if he is God all along? He had to be made like us in every respect - being a God/man is not like us at all!
Therefore he had to be made like his brothers in every respect, so that he might become a merciful and faithful high priest in the service of God
Notice Jesus is also serving God!
We are told Jesus was 'filled with the spirit' Luke 4:1. God cannot be filled with spirit - He IS spirit, Jesus said he was not spirit. Luke 24:39
The question appropriately highlights the conundrum we are faced with when using traditional understanding to interpret the bible - rather than simply reading what it says. The OP is correct in calling Jesus 'a finite body', mortal - which is what Jesus had prior to his resurrection - then he was raised immortal.
...put to death in the flesh, but made alive in the spirit... 1 Pet 3:18
*assuming 'Jesus' is the body spoken of re the tag, 'life-of-Jesus'