So, up until recently in the series, just what is the Thousandfold Thought has been debatable, but I think at this point, it is clearly (relatively, at least) established.
The main supposition of the Thousandfold Thought is that the world should be saved. This in itself is a pretty big supposition for a Dunyain to make, assuming that they're beyond their survival instincts. There are I think two versions of the Thousandfold Thought, at this point.
1. Moenghus's version. Moenghus was very much a classical Dunyain; though the world taught him many things, as far as we could tell, he remained loyal to the Dunyain ideology with one exception (his belief in that the Dunyain's millenial pursuit of ridding themselves of the Legion Within hasn't succeeded, that in subtle ways, they're still slaves to the Darkness That Comes Before). We don't know precisely how he thought the world should be saved; he clearly engineering his son's possession of the Three Seas, so we might guess that the Great Ordeal was also his endgame. Why did he think that the world should be saved? I don't know if he clearly explains this, but my guess is, being still loyal to the Dunyain ideology, he sought to save the world so that his (and perhaps, other Dunyain's) pursuit of the Absolute could continue uninterrupted*. I think we can say that this version of the Thousandfold Thought was faulty at its core, because it didn't consider the fact Moenghus and the Dunyain were damned; it's pretty much certain that if he was made to witness the Inverse Fire, he would've given up on the Thousandfold Thought and defected to the Consult.
*It's entirely possible that the Dunyain would simply keep living, remain unnoticed, had the Second Apocalypse began without any Dunyain involvement (though, we now know that the soul of an Anasurimbor was required to resurrect the No-God, so this was not truly possible but merely a hypothetical). However, the Dunyain's pursuit of the Absolute is a generational one, so Moenghus would've likely considered the need for Dunyain re-production, and thus deemed that the Second Apocalypse needs to be averted.
2. Kellhus's version. Kellhus has spent twenty years refining and expanding his father's Thousandfold Thought; and I think much of the methodology he used up until reaching the Consult was what his father envisioned. The main difference began with Kellhus's greater understanding of the metaphysical forces on Earwa - he understood damnation and hell. As the portions of the book about this were unclear, we can't be certain, but he seems to have either struck a deal with Ajokli, or even become Ajokli, and sought to conquer and enslave hell. Now, whether his version of the Thousandfold Thought failed or not is debatable:
a) Strictly regarding the Consult, he accurately predicted that it'd be taken over by the Dunyain, and seemed perfectly capable of combatting them. So, in the sense of the Thousandfold Thought being about preventing the world's destruction by the Consult, the Thousandfold Thought was successful... up until the introduction of an unstable element in the form of Kelmomas, which is what led to its apparent failure. Buuut:
b) The nature of the Inverse Fire. Now, this is strictly a theory and I mostly read these novels for entertainment, so I can't say that I am as a deep an analyst as some of the readers. I believe that in the last book, the explanation of the Inverse Fire is that when you see yourself in hell, you experience it more as a memory, as something that you remember, rather than something you're shown. My theory about hell is that it is beyond time and space and therefore, not bound by the linearity in which we experience time. People see themselves in hell, more than see, they experience it, because they're already in hell - what will happen has, in hell's context, already happened. This is significant, because Kellhus sees himself not as another soul suffering in hell, but some kind of a reaper there. For this reason, I think we can't conclude that Kellhus's Thousandfold Thought has failed; it might've, but in a convoluted way that even Kellhus himself hasn't fully figured out, it might've succeeded in reaching him to the Absolute or a near approximation of it that is, as he describes, a hunger descending on hell.
But an alternate theory as regards to this is that, "the hunger" Kellhus perceives himself to be is the No-God; when he looks at the Inverse Fire, he sees is his ultimate destiny of becoming the No-God, something that his brothers in the Consult sought to enforce upon him (and presumably succeeded; though it might've been Kelmomas instead. We really need to know more.)
A minor caveat I'd like to make is that there is a third character that professes a comprehension of the Thousandfold Thought, and that's Serwa (who may or may not be dead). I think somewhere towards the end, Serwa references to being motivated by "love, duty and honour" (or something like that) in her internal thoughts. We know that Serwa, unlike her father and grandfather, is closer to being a human as we understand it. We don't know if Serwa's interpetion of the Thousandfold Thought significantly differs from other interpretions; presumably, she would not be up for the woe Kellhus implies he'll bring upon humanity, and that she is not motivated by Moenghus's Dunyain pursuit of the Absolute and is instead motivated by more humane reasons. I don't imagine this version of the Thousandfold Thought (if it is truly distinct, at all) will be influential if the character is dead, so we'll see more about it if she survives.
Anyway, what are your thoughts on the Thousandfold Thought? It's amusing to think that so far, almost the entire story was a product of it, with Moenghus calling on Kellhus to kickstart it. Perhaps it will still hold influence, or perhaps the world and all the gods and god-like beings that prey upon it were too great to be fathomed. We'll find out more soon, I hope (though I dread it might take many years!)