  We study the fluctuations of the two-time dependent global roughness of
finite size elastic lines in a quenched random environment. We propose a
scaling form for the roughness distribution function that accounts for the
two-time, temperature, and size dependence. At high temperature and in the
final stationary regime before saturation the fluctuations are as the ones of
the Edwards-Wilkinson interface evolving from typical initial conditions. We
analyze the variation of the scaling function within the aging regime and with
the distance from saturation. We speculate on the relevance of our results to
describe the fluctuations of other non-equilibrium systems such as models at
criticality.
