You are very correct that to have a temptation enter our thoughts is not sin. Jesus Himself was presented with temptation, so that is answer enough if anyone disagrees.
What we do with the thought from there dictates when it becomes sin. To recognize it and judge it as sin and reject it - is not sin. Though even so, the depravity of even just temptation can move us slightly out of the peace of God, and we might wish to avoid even that if we are extremely sensitive.
let's pause here for a brief moment so that we can effectively communicate. You talk about the depravity of even just temptation can move us slightly out of the peace of God....I can go along with that, yet Christ demonstrated how we should be living in the power of the HS and what did He do when tempted? He drew closer to God didn't He? If He is our example, then we should by the power of the HS draw closer to God throughout temptation...The question on the table is, is it possible to face temptation and not sin for one or more days...Christ did it after 40 days of fasting...and He did it in the power of the Living God, the same Living God that dwells within us. So how then, if Christ is our example, can we say it is impossible...especially if we understand that He was both fully man and fully God....we can say that we don't, but we cannot say that we can't.
Beyond that are degrees of interaction with the temptation. If we reach the point of interacting with the thought, cozying up to it, welcoming it into our spirit, even relishing the idea of it (a very common temptation here is revenge or retaliation or "telling someone off" for something they've done that offended us) - even if we don't actually speak the words or change our minds before we act on it, we have committed sin by that point.
I would say that any interaction with temptation beyond taking the thought captive and putting the thoughts on the things of God is sin...but I could be convinced I am wrong especially since our thoughts are "lightening" fast it would be hard to say, this millisecond is not sin but that millisecond isn't which I am content with allowing God to define....
There's a very good podcast on that here if you or anyone is interested, and I'm sure it explains better than I am managing to do.
The Six Stages of Temptation - Acquiring the Mind of the Church | Ancient Faith Ministries
I am listening to the end of this, before I say more...thank you for submitting it. My husband listened to part of it and said that he could see some people's heads exploding...lol
Here is what I will say...some 12 ish years ago, God called me to full time study of Biblical Love...full time as in 40 + hours a week. In the midst of that study I did two important studies to the question on the table, one was the schemes of Satan. Its a very interesting study that goes into a lot of details not only about how Satan tries to draw us away from God but also what scripture says we should do to avoid being drug away. Whereas the speaker is not wrong on most of what he says (some I question not because it's wrong but because I personally want all my answers to be from scripture which things LIKE making the sign of the cross is not from scripture) is spot on but he is also missing a lot of things that scripture tells us to do to tap into the power to be without sin. I am not accusing or blaming him in any way, this video is not really dealing with the same thing...what I am saying is I would love to talk to him more and show him the study God led me to.
Second thing I studied that applies to the question at hand is one I am finishing now, it's about the power of God's Love to transform us....iow's how does Gods Love transform us. It is amazing how much power is found in the Living God. Power that He gives us starting the very moment that we believe unto salvation. Way too many people- way too often underestimate the power of God in our lives and we should be ashamed everytime we place God in the boxes we have created for Him as some here have done.
It is indeed good to do as you said - take those thoughts captive to Christ. We strive to have the mind of Christ, to think on those things that are good, pure, lovely, and true.
Being practiced in this discipline is a front line defense against the fiery darts of the enemy, who takes delight in attacking us through our thoughts if we are not aware of his tactics.
It's one, there are many more....some really interesting ones come from the temptations of Christ and involve study of the word of God, memorizing the word, using the word, trusting the word, meditating on the word of God and praying.