  We show that, in nonequilibrium systems with small heat flows, there is a
time-scale dependent effective temperature which plays the same role as the
thermodynamical temperature, in that it controls the direction of heat flows
and acts as a criterion for thermalization. We simultaneously treat the case of
stationary systems with weak stirring and of glassy systems that age after
cooling and show that they exhibit very similar behavior provided that time
dependences are expressed in terms of the correlations of the system. We
substantiate our claims with examples taken from solvable models with
non-trivial low-temperature dynamics, but argue that they have a much wider
range of validity. We suggest experimental checks of these ideas.
