What will be the deal with sacrifices when there is a 3rd Temple? I don't believe in sacrificing living animals, but I think sacrificing plants or animals that died of natural causes would be fine.
Well, if animal sacrifice really was restored, one could not use an animal that died of natural causes. Nothing that is
tamei (ritually impure) could be brought into the Temple precincts, because they were kept in a high state of
taharah (ritual purity). Animals which have died from any cause except for
shechitah (kosher ritual slaughter) are
tamei, and would be forbidden in the Temple precincts.
However, we know that the Third Temple will not be built until moshiach comes. And when moshiach comes, he will have the authority to radically reinterpret, and will also know how to recreate the
urim vetumim, the mysterious tools of sacred divination that the High Priest kept inside his ritual breastplate, and using which the High Priest and the king could inquire prophetically what God's will was in certain matters. So it is not out of the question to believe that perhaps the moshiach and the High Priest of his day will make use of those tools, and of that authority, and the rituals of the Third Temple would then be different than those of the first two.
Personally, I think that we have grown out of the need for animal sacrifice. I think God instructed us to do it in ancient times, because that was the universal practice, and our people would simply not have understood how to relate to God, how to expect His forgiveness for our sins, without that kind of blood ritual. They had a hard enough time just with the basic concept of monotheism. Giving up blood sacrifice would have just been too much for them.
But we have come a long way since then. I think most human beings understand that God does not require blood, either in prayer, or in praise, or in penitence; nor should animals need to die merely for our religious rituals. My guess is that there will be no more animal sacrifices. Not everything burned on the altar was animal: there were flour and oil offerings, bread offerings, even sometimes mixtures involving wine. Perhaps we will continue to offer those. But perhaps we will simply move away from that model of offering.
The offering of bringing first fruits seems like a good ritual to preserve. There was also a water-offering, poured out before the altar on Sukkot.
But most importantly, there was also the
ketoret hasamim, the burnt incense.
I think that while blood may have been important to our ancestors, just as important was the column of smoke that arose from the altars, reaching high up into the heavens. It was said that in the days of the good kings, the Presence of God would manifest itself over the Temple in the form of a pillar of cloud that reached down from the heavens. The column of smoke from the altars reached upward, and thus in the symbol of smoke and cloud, Heaven and Earth touched, signifying for all the unique holiness of that place.
The same symbol, the same awesome sight, could be achieved only with an altar burning incense.
My personal opinion is that the animal sacrifices will simply drop away, and what will be retained is the burning of the incense.