  In the framework of the Constrained MSSM we re--examine the gravitino as the
lightest superpartner and a candidate for cold dark matter in the Universe.
Unlike in other recent studies, we include both a thermal contribution to its
relic population from scatterings in the plasma and a non--thermal one from
neutralino or stau decays after freeze--out. Relative to a previous analysis
[1] we update, extend and considerably improve our treatment of constraints
from observed light element abundances on additional energy released during BBN
in association with late gravitino production. Assuming the gravitino mass in
the GeV to TeV range, and for natural ranges of other supersymmetric
parameters, the neutralino region is excluded, while for smaller values of the
gravitino mass it becomes allowed again. The gravitino relic abundance is
consistent with observational constraints on cold dark matter from BBN and CMB
in some well defined domains of the stau region but, in most cases, only due to
a dominant contribution of the thermal population. This implies, depending on
the gravitino mass, a large enough reheating temperature. If $\mgravitino>1$
GeV then $T_R>10^7$ GeV, if allowed by BBN and other constraints but, for light
gravitinos, if $\mgravitino>100$ keV then $T_R>3\times 10^3$ GeV. On the other
hand, constraints mostly from BBN imply an upper bound $T_R \lsim {a few}x
10^8\times10^9$ GeV which appears inconsistent with thermal leptogenesis.
Finally, most of the preferred stau region corresponds to the physical vacuum
being a false vacuum. The scenario can be partially probed at the LHC.
