[Maédhros]

Very interesting I must say.

I was thinking why Sauron would even want to see into the hearts and minds of men in this way, as due to their mortality, this would be a power limited in itself. Unless his aim was purely to create a group of wraiths to do his bidding. Perhaps this is why he so desired to see into the hearts and minds of immortal Elves; he would have an everlasting link into their thoughts.

Perhaps there is another motif as to why Sauron would want to have men as his slaves in this way. Consider that because of Men are mortal, their hröa would eventually die and their fëa would leave the world, those cannot be such great servants if they leave eventually but if you somehow could prevent their fëar leavin the world (ex: by somehow linking Sauron's own spirit to the fëar of men) to prevent that men would enjoy the gift of Eru in order to make men slaves forever.

What is interesting in the above passage is how it specifically mentions that the Three had to be concealed. Was there some faint or tenuous connection between the One and the Three which may have enabled thought transference between Sauron and those who bore these rings? I cannot be certain, but is it the case that they were not used until the Ruling Ring was known to be lost? That they in themselves in some way possessed qualities which may have enhanced those discussed in Osanwe-Kenta is a possibility raised in the following sentence which says that no ‘open’ word was ‘spoken’:

Perhaps because the rings came from the same kind of craft, the ringbearers had greater affinity than otherwise they would have had. We also have to remember that it was not the later elven ring bearers but Celebrimbor who noticed what Sauron was up to. I don't think that there can be a greater affinity between the maker of the 3 rings and Sauron, both great craftsmen in their own right.

That he was unable to control the thoughts of the Elves is due to their own innate abilities, and they ‘saw’ what he was attempting to do. While Men were not aware of what he would do, maybe because their power of thought was latent?

The thing is that, if the One ring could control the mind of the ring bearers, how is it that Celebrimbor was able not to fall into Sauron's control? Does that means that Sauron needed sometime to get used to using the ring to control others?

I think that the bigger question that needs to be asked is this:
How could Sauron control minds of Elves that not even Morgoth could? How could Sauron control the minds of others if that is an impossibility? Only Eru can open a closed mind?
I wonder if that means that Sauron could leave open the minds of other beings by deceiving them with their desires?
Elves (ñoldor) = Valinor in ME.
dwarves = riches.
Men = power.

From Ósanwe-kenta

The Incarnates have by the nature of sáma the same faculties; but their perception is dimmed by the hröa, for their fëa is united to their hröa and its normal procedure is through the hröa, which is in itself part of Eä, without thought. The dimming is indeed double; for thought has to pass one mantle of hröa and penetrate another. For this reason in Incarnates transmission of thought requires strengthening to be effective. Strengthening can be by affinity, by urgency, or by authority.
Affinity may be due to kinship; for this may increase the likeness of hröa to hröa, and so of the concerns and modes of thought of the indwelling fëar, kinship is also normally accompanied by love and sympathy. Affinity may come simply from love and friendship, which is likeness or affinity of fëa to fëa.
Urgency is imparted by great need of the "sender" (as in joy, grief or fear); and if these things are in any degree shared by the "receiver" the thought is the clearer received. Authority may also lend force to the thought of one who has a duty towards another, or of any ruler who has a right to issue commands or to seek the truth for the good of others.
These causes may strengthen the thought to pass the veils and reach a recipient mind. But that mind must remain open, and at the least passive. If, being aware that it is addressed, it then closes, no urgency or affinity will enable the sender's thought to enter.

Though in "Arda Unmarred" openness is the normal state, every mind has, from its first making as an individual, the right to close; and it has absolute power to make this effective by will. Nothing can penetrate the barrier of Unwill.

Just to make a note:

With this statement of the impossibility of forced penetration of the mind, compare the first paragraph of part (ii) of the Notes on motives in the Silmarillion (MR:398-99), which appears to say that such an act is possible, though forbidden and, even if done for "good" purposes, criminal.

The interesting thing is that while Melkor used his powers to control others by the use of the language, could Sauron have refined this method by somehow using the rings?