I do believe there is a difference between having a thought and living with a thought!
There is no sin in noticing attractive women. Women are God's creation. And we have to hold God the Creator responsible for the human attractiveness.
So it is not the SEEING which Jesus speaks to.
It is the gazing with an evil intention.
It is not the first look. It is the second look with intent -
"to lust after her".
In other words, it is not the first step of seeing that He convicts of.
It is the step of intentionally gazing with an evil intent Christ exposes as the heart problem. It is the second look with the third step
" ... looks at a woman IN ORDER TO ... lust after her ..." .
If you are fairly typical man and reading this causes you to say "Fellas, we're finished !"
then you have gotten that point right. However throughout the Gospel of Matthew we should hang on to the introductory remarks about Jesus.
" And she [Mary] will bear a son, and you shall call His name JESUS, for it is He who shall save His people from their sins." (Matt. 1:21)
1.) We have to become among
"His people".
2.) We may trust that He will save
"His people" from their sins - within and without.
That He will save His people from the guilt of sin is seen in His redemptive sacrifice.
" For this is My blood of the covenant, which is being poured out for many for forgiveness of sins." (Matt. 26:28)
He died to remove the guilt of sins.
And He plants Himself into man as
"the word of the kingdom" to supply the life power to save His people from the power of the sin nature.
We can deduce this in many places. One I refer to is His parable about the seed of the kingdom in the four kinds of soil. The soil representing the heart of man. And the last cultivated soil, with rocks and thorns dealt with and removed, allows the life seed of His teaching to grow and bear fruit.
" But others [seeds] fell on good earth and yielded fruit, one a hundredfold, and one sixtyfold, and one thiryfold." (13:8)
And His corresponding brief interpretation of this saying.
"But the one sown on the good earth, this is he who hears the word and understands, who by all means bears fruit and produces, one a hundrefold, and one sixtyfold, and one thirtyfold." (13:23)
The bearing of fruit for the kingdom has to be the growing of righteous living, godly living, living expressing the indwelling Christ from a human heart kept, cultivated, cared for. And you alluded to the Proverb about keeping one's heart.
The point of this post is that the demand of the kingdom life is very high.
But the supply to meet the demand is very effective, full of powerful life, and fruitful to produce value for God's righteous kingdom.
Being tempted isn't a sin, but lusting after is so acknowledging the neighbor's wife is
attractive in one's thought life doesn't mean that you are spending your time desiring
her, you cross that line when you spend your time doing just that.
It is true that we can be too introspective and feel overly guilty.
To the Christian who is growing normally, he will allow the Holy Spirit to go deeper and deeper into his life, trusting that Jesus can grant us self control.
At first he sees trouble when it is up in his face.
As he grows, he sees trouble coming a mile away.
At first the outward action he confesses as a sin to be repented of.
As the Holy Spirit deepens His influence over his heart, he because more sensitive.
He pulls his mind back from wrong thinking as a hand is pulled back from fire.
He sees trouble coming way, way down the road.
The anger, the lust, the love of self, the hypocrisy, the anxiety, the self pity, and all the things infesting the fallen nature, Christ is a Great Physician to heal from.
Instead of pouting like athiest Christopher Hitchens that God is like a dictator from North Korea, we are relieved and comforted that Christ is a wonderful Doctor who can care and heal and liberate on such a low even subconscious level.
What a Savior !