"…who were the sons of Levi mentioned in Malachi 3:3 who were to be purged as gold and silver that they might offer unto the Lord an offering in righteousness?…In Doctrine and Covenants 128:24 we apparently have the answer…
'Behold, the great day of the Lord is at hand; and who can abide the day of his coming, and who can stand when he appeareth? For he is like a refiner's fire, and like fuller's soap; and he shall sit as a refiner and purifier of silver, and he shall purify the sons of Levi, and purge them as gold and silver, that they may offer unto the Lord an offering in righteousness. Let us, therefore, as a church and a people, and as Latter-day Saints, offer unto the Lord an offering in righteousness; and let us present in his holy temple, when it is finished, a book containing the records of our dead, which shall be worthy of all acceptation.' (D&C 128:24)
"The Latter-day Saints as a Church and a people seem to be the ones who are to offer up an offering in righteousness in the temple in the form of a book containing the records of our dead. They are, therefore, the sons of Levi who are to be purged as gold and silver. When John the Baptist did come at a later time (15 May 1829) to Joseph Smith and Oliver Cowdery, and conferred upon them the keys of the Aaronic Priesthood, he made special mention of the fact that, 'This [the Aaronic Priesthood] shall never again be taken from the earth, until the sons of Levi do offer again an offering unto the Lord in righteousness' (D&C 13:1). John seems to have been especially concerned with the sons of Levi. Again in Doctrine and Covenants 84:31–34, we find material pertinent to Malachi's prophecy:
'Therefore, as I said concerning the sons of Moses-for the sons of Moses and also the sons of Aaron shall offer an acceptable offering and sacrifice in the house of the Lord, which house shall be built unto the Lord in this generation, upon the consecrated spot as I have appointed-
And the sons of Moses and of Aaron shall be filled with the glory of the Lord, upon Mount Zion in the Lord's house, whose sons are ye; and also many whom I have called and sent forth to build up my church.
For whoso is faithful unto the obtaining these two priesthoods of which I have spoken, and the magnifying their calling, are sanctified by the Spirit unto the renewing of their bodies.
They become the sons of Aaron and the seed of Abraham, and the church and kingdom, and the elect of God.' (D&C 84:31–34)
"In these verses it is again to be noted that the sons of Moses and of Aaron are to offer an acceptable offering and sacrifice in the house of the Lord. Those who hold the Aaronic and Melchizedek priesthoods are indeed the sons of Levi and are the ones whom Malachi apparently had in mind when he gave his great prophecy. In making this statement, we do not wish to exclude any of the literal descendants of Levi who may later come in the Church and perform temple work. It is apparent then that Moroni began his explanation of temple work and of salvation for the dead in connection with Malachi 3, rather than with Malachi 4, as so many in the Church commonly suppose." (FARMS: Journal of Book of Mormon Studies, vol. 4, no. 1, Spring-1995, pp. 273-4)
The above quotation is helpful, but we should not conclude that Malachi was only referring to Melchizedek priesthood ordinances. The ordinances of the Aaronic Priesthood will also be restored as part of the restitution of all things. Therefore, when the New Jerusalem Temple is built, ordinances of the Aaronic priesthood will be performed by "the sons of Levi," and this includes the ordinances of animal sacrifice.
Joseph Smith
"These sacrifices, as well as every ordinance belonging to the Priesthood, will, when the Temple of the Lord shall be built, and the sons of Levi be purified, be fully restored and attended to in all their powers, ramifications, and blessings. This ever did and ever will exist when the powers of the Melchizedek Priesthood are sufficiently manifest; else how can the restitution of all things spoken of by the Holy Prophets be brought to pass? It is not to be understood that the law of Moses will be established again with all its rites and variety of ceremonies; this has never been spoken of by the prophets; but those things which existed prior to Moses' day, namely, sacrifice, will be continued.
"It may be asked by some, what necessity for sacrifice, since the Great Sacrifice was offered? In answer to which, if repentance, baptism, and faith existed prior to the days of Christ, what necessity for them since that time? The Priesthood has descended in a regular line from father to son, through their succeeding generations." (Teachings of the Prophet Joseph Smith, p. 173)
Joseph Fielding Smith
"It should be remembered that the great temple, which is yet to be built in the City Zion, will not be one edifice, but twelve. Some of these temples will be for the lesser priesthood.
"When these temples are built, it is very likely that provision will be made for some ceremonies and ordinances which may be performed by the Aaronic Priesthood and a place provided where the sons of Levi may offer their offering in righteousness. This will have to be the case because all things are to be restored…The sacrifice of animals will be done to complete the restoration when the temple spoken of is built; at the beginning of the millennium, or in the restoration, blood sacrifices will be performed long enough to complete the fulness of the restoration in this dispensation. Afterwards sacrifice will be of some other character." (Doctrines of Salvation, 3:93-4 as taken from Latter-day Commentary on the Book of Mormon compiled by K. Douglas Bassett, p. 451)