  In this paper we present a short survey on the concept of effective
temperature, on its onset as a glass former vitrifies, on the various
definitions in literature and their limits of applicability. An exactly
solvable model glass is employed to compare effective temperatures among them
and to set a criterion for the occurrence of a universal extra temperature in
the framework of a "two temperature thermodynamics" for off-equilibrium aging
systems. It will be shown that aging in glass formers is not a sufficient
requirement. As an instance, memory effects typical of glasses are not
compatible with a unique effective temperature. Yet, a reduced range of
applicability can still be established and investigated.
