No. It clears you only of eternal punishment.
The prayer and penitential acts that you do both as part of the Sacrament and at other times (especially Mass and those prayers that carry an indulgence, which is a remission of the temporal consequences of sin) is what clears the temporal punishment.
The commonly used analogy: you hit a ball and break the neighbour’s window. You apologise to them and they forgive you (confession and absolution).
Then, to make everything right, you might fix their window yourself if you’re a handyman, pay money for it to be fixed, do chores for them to work off the value etc. That’s the prayers and penances.