It is somewhat inexact to say: Baptism removes original sin. Original sin led, among other things, to loss of sanctifying grace. What Baptism does is infuse sanctifying grace and bring our soul to life.
You mention removal of temporal punishment. That is a different idea, though. In Baptism, a Sacrament of the dead, our soul receives the life-giving Spirit for the first time. Thus, both the guilt of sin and all the penalties attached to sin are remitted.
Some of the other inherent consequences of original sin still remain with us:
- death and suffering
- concupiscence
In Baptism we become neither immortal nor impeccable. This will all happen later…there is a process we need to undergo by freely cooperate with God’s grace, which will lead to our salvation, sanctification, glorification, and even divinization.
We are justified in Baptism (CCC 1992), but as st. Paul writes, we have to “work out our salvation”, “run as to win the race”, and “discipline our body, lest we be disqualified”…orthodox Christian doctrine terms this the
processus iustificationis.
In baptism the guilt of original sin is wiped out and the soul is cleansed and justified again by the infusion of sanctifying grace. But freedom from concupiscence is not restored to man, any more than immortality; abundant grace, however, is given him, by which he may obtain the victory over rebellious sense and deserve life everlasting.
According to the orthodox doctrine reaffirmed in Trent, concupiscence remains in those that are baptized in order that they may struggle for the victory, but does no harm to those who resist it by the grace of God.
In short: it is a cross, but such is the Christian vocation, to embrace the cross and be willing to suffer, in order for us to “fill up those things that are wanting of the sufferings of Christ, in our flesh, for His body, which is the Church”.
You can read more about all of the above
here