  We present evidence in favor of the possibility of treating an
out-of-equilibrium supercooled simple liquid as a system in quasi-equilibrium.
Two different temperatures, one controlled by the external bath and one
internally selected by the system characterize the quasi-equilibrium state. The
value of the internal temperature is explicitly calculated within the inherent
structure thermodynamic formalism. We find that the internal temperature
controls the relation between the response to an external perturbation and the
long-time decay of fluctuations in the liquid.
