Answer

It is indeed difficult to connect. In my opinion, the main task during these days is not actually to mourn, but rather to try to understand why to mourn. I’ll tell you what I explain to myself: today it seems repulsive to me to hope for priests walking around knee-deep in the blood of slaughtered animals. A horrifying slaughterhouse. On the other hand, I am fully aware that I did not live in the time when there was a Temple and did not experience its significance. Therefore I cannot judge how much it is lacking. I trust the words of the Sages that this was something significant, and I mourn the fact that I do not have the ability to understand it and identify with it.
It may be that when it returns—if it returns—it will become clear to me that I was mistaken. But I want to hope that if that is indeed the case, then the Temple will not return at all. So then I would mourn the fact that I thought there was something here to mourn.
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Questioner:
So in the end, are you hoping it won’t return?
Itamar,
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Rabbi:
No. I said that on the emotional, experiential level I have no desire at all for it to return, because my feeling today is that this is something fairly repulsive. On the other hand, I am aware that I did not experience these things, and therefore I cannot really judge them and their significance from my current point of view (perhaps the sense of spirituality when there is a Temple is very meaningful and tangible, and everyone understands why it is necessary). I said that perhaps when the Temple returns it will become clear that I was mistaken in my assessment, and really it is not worthwhile for it to exist (as I feel today), but if that is really the case then I hope and believe that it truly will not return.
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Questioner:

1. In your answer you addressed one aspect of the Temple. (Personally, I connect to the lack of anticipation for such a Temple as the one longed for in the Yom Kippur prayer.) But it seems to me that the Temple is not only sacrificial worship. In its time, the sacrificial service was central because that was what was accepted in the world, or because it served as a contrast to what was accepted. In any case, in the future it could take on a different character. The problem with the difficulty of mourning for the Temple stems from the identification people make between the Temple and sacrifices.
The Temple was the religious center of the people, and as such it was a kind of status symbol for the condition of the nation.
Even if a Temple were established without sacrificial worship, it would still have meaning. For example, halakhically, Torah-level laws could be changed and interpreted by a Great Sanhedrin sitting in the Temple in Jerusalem. The Temple could symbolize our progress and our lack of stagnation (the exact opposite of a Temple as a slaughterhouse for sacrifices).
Isn’t that something to wait and hope for? (At last we could update things for our times, though on the other hand, as you said we learned in Perplexed of the Generation, they could change the thirty-nine categories and either be lenient about one form of labor or stringent about a million of them…)

2. The questioner asked about “connecting to mourning the destruction that happened 2,000 years ago, and especially to the Temple.”
It seems to me that there is a mistaken assumption here that we were educated with, and that is why this question comes up again and again, wrongly. We were taught to think that on the Ninth of Av we mourn the Temple, and it is hard to educate people to yearn for something that they do not truly miss. True, it was destroyed on the Ninth of Av, and this day is part of a series of fasts over the destruction. But from reading the Book of Lamentations and the dirges, it emerges that the main pain and mourning were over the condition of the people (both individually and collectively), not over the lack of the Temple itself.
It is much easier to connect to and mourn a terrible state of horrific famine, women eating the fruit of their wombs, severe internal conflicts that led to bloodshed, the loss of the Temple, of sovereignty, and exile. (Just as there is no difficulty connecting to mourning on Holocaust Remembrance Day; you just need to take the dirges, Lamentations, and the midrashim as black-and-white films…)
This connects to point 1, that the Temple represented the state of the nation. The internal conflicts and corruption of the leadership were very evident in the Temple, and it represented everything bad among the leadership and in the general population. So if one understands the Temple that way, there is something to mourn and something to yearn for—not necessarily the building itself, but the people then and now (*).

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(*) Many people look for the connection to our own time, trying to find how this touches me, us. I am not claiming, as is customary in the national sport, that everything here is rotten from top to bottom. But even if we are in wonderful shape compared to those days, there is certainly still much to fix in the leadership and in society, and there is something to yearn for.

Yuval S.,
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Rabbi:
Hello Yuval.
In a parallel question I did in fact add mourning over the exile and over the people.
Your first point is a dispute between Maimonides (who holds that the Temple is a place for offering sacrifices) and Nachmanides (who holds that it is a place where the Divine Presence rests). Either way, without sacrifices none of this happens (at least according to how things were then), and therefore it is hard to separate the two. Unless you want to argue that in the future we will have some sort of Buddhist temple, meaning a place for spiritual practice without sacrifices. But that already exists today: “Within my heart I will build a sanctuary.”
And the Sanhedrin is also not conditional on the existence of a Temple, so all the improvements you pointed to do not really depend on it, but mainly on us (so instead of mourning, we should simply fix things, and that’s it). Still, all this is from my current perspective, but perhaps in the future it will become clear to me that I understood it incorrectly, as I wrote.