  We investigate gravitino dark matter produced thermally at high temperatures
and in decays of a long-lived sneutrino. We consider the Non-Universal Higgs
Model and a generalized gauge mediation model, and in each case identify
sneutrino LOSP regions of the parameter space consistent with the mass of the
Higgs-like boson observed at the LHC. We apply relevant collider and
cosmological bounds, including constraints from Big Bang Nucleosynthesis and
from warm dark matter on large scale structures. Generally, we find allowed
values of the reheating temperature TR below 10^9 GeV, i.e. somewhat smaller
than the values needed for thermal leptogenesis, even with a conservative lower
bound of 122 GeV on the Higgs mass. Requiring mass values closer to 126 GeV
implies TR below 10^7 GeV and the gravitino mass less than 10 GeV.
