  Understanding glasses is considered to be one of the most fundamental
problems in statistical physics. A theoretical approach to unravel their
universal properties is to consider the validity of equilibrium concepts such
as temperature and thermalization in these out-of-equilibrium systems. Here we
investigate the autocorrelation and response function to monitor the aging of a
colloidal glass. At equilibrium, all the observables are stationary while in
the out-of-equilibrium glassy state they have an explicit dependence on the age
of the system. We find that the transport coefficients scale with the
aging-time as a power-law, a signature of the slow relaxation. Nevertheless,
our analysis reveals that the glassy system has thermalized at a constant
temperature independent of the age and larger than the bath, reflecting the
structural rearrangements of cage-dynamics. Furthermore, a universal scaling
law is found to describe the global and local fluctuations of the observables.
