Do any Christian traditions think that evil desires are not sin?

Would it have possible for Jesus to sin ? NO. Would it be possible for him to have had evil thoughts? No'

Matthew 1;18

Now the birth of Jesus was on this wise: When as his mother Mary was espoused to Joseph, before they came together, she was found with child of the Holy Ghost.

John 3;5

Jesus answered, verily, verily, I say unto thee, Except a man be born of water and the Spirit, he cannot enter into the kingdom of God.

Philippians 2;7-8

But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men; 8 And being found in fashion as a man, he humbled himself, and became obedient unto death, even the death of the cross.

From the beginning, Jesus was converted, being born of water ( naturally, through Mary ) and the Spirit (Holy Ghost),

Matthew 18;3

And said, verily, I say unto you, Except ye be converted and become as little children, ye shall not enter into the kingdom of heaven.

Hebrews 4;15 For we have not an high priest which cannot be touched with the feeling of our infirmities; but was in all points tempted like as we are, yet without sin.

Hebrews 5;9 And being made perfect, he became the author of eternal salvation unto them who obey him.

Jesus, through the power of his Father, and obedience to his will, overcame all temptation without yielding to sin. Jesus is the perfect high priest, sinless and eternal. His character is flawless. Temptation, is a test of character.

Man is born of water and decended from Adam (man).

Psalms: 51;5

Behold, I was shapen in iniquity, and in sin did my mother conceive me.

Jeremiah 17;9

The heart is deceitful above all things, and desperately wicked: who can know it?

Matthew 5;28 But I say unto you, That whosoever looketh on a woman to lust after her hath committed adultery with her already in his heart.

1 John 3;9 Whosoever is born of God doth not commit sin, for his seed remaineth in him and he cannot commit sin, because he is born of God.

I heard a priest say that temptation and evil desires are not themself sinful, but rather how one acts. Indeed to have evil desires and temptation and not to give in to them would then be considered virtuous.

In Judaism, this would be an easy question. Only actions count. Harboring the most evil thoughts one could imagine is not a sin by itself. It's only when one acts on those thoughts that they retroactively become sin.

For instance, being a h*m*sexual is not a sin, it is simply a part of what one is; but behaviour resulting from those desires is a sin.

In Christianity it is different. Jesus introduced the spiritual aspect of his laws:

You have heard that it was said to those of old, ‘You shall not murder, and whoever murders will be in danger of the judgment.’ But I say to you that whoever is angry with his brother without a cause shall be in danger of the judgment.
…
You have heard that it was said to those of old, ‘You shall not commit adultery.’ But I say to you that whoever looks at a woman to lust for her has already committed adultery with her in his heart.
— Matthew 5:21–22,27–28

It is no longer enough to obey the letter of the law; a Christian must obey the spirit of the law. Wanting to sin is a sin in itself.

After seeing a beautiful woman, one can:

• Feel pleasure, the same way one would appreciate an impressive sunset or enjoy watching puppies playing in a park.
• Feel physical desire.
• Feel lust and imagining acting on that lust.
• Feel lust and physically acting on that lust.

Under God's physical law, only the last case would be considered a sin.

Under God's spiritual law, the last two (lust) would be sin, while the second (desire) would be a state that one is expected to recognize as temptation and to immediately change. Recognizing and appreciating beauty while also respecting what is and is not appropriate is the ideal response.

Temptation (the second case above) is a necessary part of life. Learning to quickly recognize it, and then to immediately resist it, is an important way in which people strengthen and grow their spiritual character.

… the question of whether Jesus had evil desires

By definition, "evil" is sin, so no Jesus never had an evil desire.

Jesus did however experience potentially wrong emotions. For instance he demonstrated anger at those conducting business in the Temple:

When He had made a whip of cords, He drove them all out of the temple, with the sheep and the oxen, and poured out the changers’ money and overturned the tables. And He said to those who sold doves, “Take these things away! Do not make My Father’s house a house of merchandise!”
— John 2:15–16

But it was not "without a cause". His feeling anger was justified, and he acted on it not out of hatred or a desire to hurt, but by causing fear in order to get them to stop.

Within Christianity, intent is an important factor with respect to someone's actions.

Baptists believe that being tempted is not sinning, for two reason, the first being because of James 1:13-15.

"Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man: 14 But every man is tempted, when he is drawn away of his own lust, and enticed. 15 Then when lust hath conceived, it bringeth forth sin: and sin, when it is finished, bringeth forth death. " James 1:13-15 (KJV)

This verse indicates that sin doesn't occur until after you are tempted. Another reason is the fact that Jesus was tempted and did not sin. (mark 1:24 says Jesus is the Holy one of God, indicating that Jesus is holy)