The writer of Hebrews makes this amazing claim regarding Jesus:
For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yet without sin. (Hebrews 4:15, NASB)
This is very comforting to know that Jesus understands our plight and struggle with temptation, yet did not fall to temptation. Since He conquered sin, He was able to offer Himself as the sinless Lamb of God on our behalf that we might be forgiven through faith in His blood (Rom. 3:25). It also good to know that because He conquered temptation, we can conquer temptation through Him.
But something seems a little off in what the writer of Hebrews is saying. Can Jesus really relate to our struggle with temptation? Isn’t there a significant difference? I believe that Philippians 2:5-8 makes it clear that Jesus did not rely on His deity to overcome sin or remain steadfast in His mission. Instead, He relied on prayer and the power of the Holy Spirit, just as we can. But there is still a major difference. Jesus did not have to deal with the inward pull of the sinful nature. He had no sinful nature.
We can say that Jesus resisted external temptation (like from the devil in the wilderness), but can we say He resisted internal temptation? If not, how then can we look to Him as an example to follow and a champion of resistance against sin that we can emulate? How can Jesus relate to the powerful inward pull of the sinful nature in temptation without having a sinful nature? The writer of Hebrews isn’t saying that our struggles and Jesus’ struggles are exactly the same (Jesus doesn’t face all the same struggles we do, but we don’t face the same struggles Jesus did either. Indeed, Jesus faced intense struggles that no man can properly relate to). So it is not meant to be an exact comparison as far as the specifics of temptations we might face in life, though it does seem to plainly be a deliberate comparison regarding the “sorts” of temptations and struggles we might face in life. But still, how can Jesus relate to both internal and external temptation without the presence of the sinful nature?
I think the first clue may be found in the narrative of the wilderness temptation. Jesus commits himself to fasting for 40 days in the desert (and presumably praying). In Matthew 4:2, we are told something that should go without saying: “he was hungry.” Talk about an understatement! Forty days without food would certainly create a strong hunger. Indeed, one would feel like they were starving to death. We immediately see that Satan’s first temptation attacks Jesus’ internal weakness of being hungry, “If you are the Son of God, tell these stones to become bread” (vs. 3). Here is a powerful lesson on the nature of Jesus’ temptation.  It wasn’t only external, but internal. Jesus never faced the internal pull of the sinful nature, but He did face the internal pull of intense hunger and desire for food. This internal pull was in no way sinful. It was natural to His humanity, but also unnatural as it was such an extreme hunger resulting from 40 days without food. So this internal pull was very powerful, yet innocent. However, if Jesus gave into His hunger at this moment it would have resulted in sin. So in the wilderness temptation we have at least one example of powerful outward and inward temptation being faced and conquered by Christ.
Another example would be in the garden before Jesus’ arrest. Jesus was dealing with a great deal of internal fear and anxiety over the events that He was about to endure. The Bible makes this extreme level of anxiety very clear in Luke where it tells us that he sweat drops of blood (Luke 22:44). We know that this is a description of a rare, but real medical condition called “hematidrosis” or “hemohidrosis.” It is the result of tiny capillaries in the sweat glands rupturing and can be brought on when someone is under extreme duress. Jesus was again experiencing extreme internal pull to avoid the mission God had set for Him to accomplish. This pull is further manifested in His prayer to the Father, that if there be any other way to accomplish His redemptive work, that the Father take away this “cup” of extreme suffering He was about to endure. But once again, though Jesus faced this strong internal pull to retreat from His divinely appointed mission, He still conquered temptation once again in fully submitting His will (and His human weakness) to the will of the Father. 
For these reasons, I think we can fully affirm what the writer of Hebrews is saying. Even though Jesus did not have to deal with the inward pull of the sinful nature while resisting temptation, He did have to deal with tremendous internal temptation as well as external temptation, and was “yet without sin.” What a marvelous Savior and High Priest, familiar with our weaknesses and an “ever present help in our time of need.” (Heb. 4:15-16, cf. Psalm 46:1)
 My guess is that this is not a novel interpretation of this difficult passage, though I don’t recall having personally ever read anyone take this particular approach.
 These are just two representative examples plainly expressed in Scripture. No doubt there were many other times Jesus faced and overcame internal temptations without those temptations needing to have arisen from a sinful nature, which Christ did not possess (whether recorded in Scripture or not).