ROY - Will the temple work be done for all the people who ever lived on earth or everyone who will live on earth, with the exception of those who died before becoming accountable?

JOEL - Mostly it will only be done for those who have accepted the gospel in the Spirit World. The scriptures say:

"All who have died without a knowledge of this gospel, who would have received it if they had been permitted to tarry, shall be heirs of the Celestial Kingdom of God;" (D&C 137:7)

All of these people will need temple work done for them. But right now since we don't know who would have accepted it, we are asked to search out our own ancestors and do the work for all of them regardless of whether we think they would have accepted it or not.
But that will change after the Second coming. During the Millennium, when the veil has been lifted, we will be able to receive information about those who have accepted the Gospel in the spirit world and we will only need to do the work for them and not for those who did not accept it.
According to President Joseph Fielding Smith:
"By the time Christ comes we are expected to have done all that is within our power to do now for our dead. That does not mean we are going to do all that is to be done, because it will go on during the millennium.
The great work of the millennium will be the salvation of the dead, and those who are on the other side will help us, too, by bringing us information. The ordinances for the salvation of the dead are mortal ordinances, because all these ordinances pertain to this life, and immortal beings cannot perform them.
Those who will be living here then will be in daily communication with those who have passed through the resurrection, and they will come with this information, this knowledge that we do not have and will give it to those who are in mortality saying,
"Now go into the temples and do this work; when you get this done, we will bring you other names." And in that way every soul who is entitled to a place in the celestial kingdom of God will be ferreted out, and not one soul shall be overlooked. (Doctrines of Salvation, Vol. 2)

So during the millennium it will be a little easier in the sense that we will know in advance exactly who to do the work for and not waste time on those who never accept it. But for now we are asked to do it for all our ancestors.

It is possible that at some future time, perhaps during the Milennium, that even children who died before turning 8 will be baptized, to fulfill all righteousness as Jesus did, and receive temple endowments. But precisely what the Lord will require in the form of ordinances, or other requirements, for spirits who died as infants or children on earth in order to receive exaltation has not been revealed. It is certain that we do not currently endow children who die before accountability nor do we seal them to a spouse. But this does not mean that the blessings of these latter ordinances are unavailable to them. President Joseph Fielding Smith also said:

"The Lord will grant unto these children the privilege of all the sealing blessings which pertain to exaltation.
We were all mature spirits before we were born, and the bodies of little children will grow after resurrection to the full stature of the spirit, and all the blessings will be theirs through their obedience the same as if they had lived to maturity and received them on the earth.
The Lord is just and will not deprive any person of a blessing, simply because he died before that blessing can be received. It would be manifestly unfair to deprive a little child of the privilege of receiving all the blessings of exaltation in the world to come simply because it died in infancy." (Doctrines of Salvation, Vol. 2)