In D&C 138:57-59 it states:
"the faithful elders from this dispensation, when they depart this life continue their labors by preaching to those who are in darkness and under bondage of sin, etc."
The scripture then says that the dead who REPENT WILL BE REDEEMED, THROUGH OBEDIENCE TO THE ORDINANCES OF THE HOUSE OF THE LORD. I thought temple ordinances, including baptisms for the dead, were only necessary for those who are heirs to at least some degree in the Celestial Kingdom. See Doctrines of Salvation, II, p. 191. If this is so, then why does the scripture go on to say "[a]nd after they have paid the penalty of their transgressions, and are washed clean, shall receive a reward according to their works, for they are heirs of salvation."
If they repent and are redeemed through the ordinances of the temple then why are they paying the penalty for their transgressions? I understood D&C 19:15-18 to mean if you repent then because of the atonement you do not suffer because Christ suffered for us. As I read this scripture it can only mean one of two things. First, some people who end up in he Celestial Kingdom must suffer for their own sins. Second it could mean that these people are not going to the Celestial Kingdom ("for they shall receive a reward according to their works"). So am I wrong that an "heir of salvation" (not "exaltation") can end up in the C, T or T Kingdom, as all are kingdoms of glory and the heirs of each of these kingdoms are saved with a "resurrection of endless life and happiness"? (Mosiah 16:11) And if so then why did they need the ordinances of the temple?
To enter into the Celestial Kingdom requires the ordinances of the Temple. As explained in D&C 131: 1-4:
1 In the celestial glory there are three heavens or degrees;
2 And in order to obtain the highest, a man must enter into this order of the priesthood [meaning the new and everlasting covenant of marriage];
3 And if he does not, he cannot obtain it.
4 He may enter into the other, but that is the end of his kingdom; he cannot have an increase.
This statement defines the "highest" as the only one involving the covenant of marriage. The other Celestial Kingdom residents would require all Temple ordinances, from washings, anointings through endowment to be able to enter and pass by the sentinels who stand guard there. Only the highest requires the new and everlasting covenant of marriage.
As to who will "suffer for their own sins" and yet enter into the Celestial Kingdom, there are at least two categories: First, those who have received their calling and election, but who return to sin, but not an unpardonable sin. Those are required to "pay the price" for this misconduct. (D&C 132: 26.) Second, those who are "sealed up" through the faithfulness of their parents, who claim them as children of promise as a matter of right because of the sealing upon the parents. Such children will need to either qualify in their own right, or if inheritors of the promise through the merit of their parents' sealing they will have to suffer to become clean in order to inherit what is sealed upon them by this right.
It is a good question. It shows the order in heaven and the way in which things are governed by laws established before the foundation of the world. (D&C 130: 20-21.)