Furthermore, no one not eating for 39 days would be able to walk out of the wilderness under their own power...
Jesus was not going to die before the appointed time, nor was He going to fail in any purpose He had from God the Father. What may or may not satisfy the thoughts of man are less important than the purpose and provision for fulfilling God's perfect will.
As far as what anyone may be capable of doing, it is important to note there is physical strength that comes from God, and there is special provision made by God that goes to providing strength in unusual circumstances.
I Kings 19
8 And he arose, and did eat and drink, and went in the strength of that meat forty days and forty nights unto Horeb the mount of God.
As far as Jesus being able to survive, walk out of the wilderness etc., (maybe the woods, but not likely a desert,) it is as it was with Elijah when fleeing Jezebel. God sent angels, just as Satan had referenced. This same thing happened in the Garden of Gethsemane, in order for Jesus to endure till all was finished. He certainly did not remain any longer than necessary, but DEFINITELY was given strength to endure to the performance of what was needed, and prescribed by God.
Matthew 4
11 Then the devil leaveth him, and, behold, angels came and ministered unto him.
Luke 4
2 Being forty days tempted of the devil. And in those days he did eat nothing: and when they were ended, he afterward hungered.
Mark 1
13 And he was there in the wilderness forty days, tempted of Satan; and was with the wild beasts; and the angels ministered unto him.
In the garden, at the arrest of Jesus, He stated that he could call 12 Legions of angels for defense. God certainly made all necessary provision for Jesus the Son of God, and Son of Man, to fulfill His purpose while here.
Luke 22
43 And there appeared an angel unto him from heaven, strengthening him.
Further, it is important to note that Jesus Christ was not killed on the cross. He lay down His life freely, and gave up living His physical life when He had finished His purpose.
John 10
18 No man taketh it from me, but I lay it down of myself. I have power to lay it down, and I have power to take it again. This commandment have I received of my Father.
John 19
30 When Jesus therefore had received the vinegar, he said, It is finished: and he bowed his head, and gave up the ghost.
John 19
35 And he that saw it bare record, and his record is true: and he knoweth that he saith true, that ye might believe.
John 20
31 But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.
These are not simply thoughts, nor is it conjecture to take God at His word. It is a sure foundation, and any of us is doing well to believe the record of God on the subject.