  We examine a scenario in which the reheating temperature $T_R$ after
inflation is so low that it is comparable to, or lower than, the freeze out
temperature of ordinary WIMPs. In this case the dark matter relic abundance is
reduced, thus relaxing the impact of the usually strong constraint coming from
the requirement that the universe does not overclose. We first re-examine the
dynamics of freezeout during reheating. Next we apply a Bayesian approach to
study the parameter space of the MSSM with ten free parameters, the CMSSM and
the singlino-dominated regions of the NMSSM. In each case we find dramatic
departures from the usually considered regime of high $T_R$, with important
implications for direct detection dark matter searches. In the MSSM we examine
WIMP mass range up to ~5 TeV, and find regions of bino dark matter over the
whole mass range, and of higgsino dark matter with mass over a similar range
but starting from the ~1 TeV value of the standard high $T_R$ scenario. We show
that the prospects for bino detection strongly depend on $T_R$, while the
higgsino is for the most part detectable by future one-tonne detectors. The
wino, which is excluded in the standard scenario, becomes allowed again if its
mass is roughly above 3.5 TeV, and can be detectable. In the CMSSM, the bino
and higgsino mass ranges become more constrained although detection prospects
remain similar. In the Next-to-MSSM at low enough $T_R$ wide ranges of
singlino-dominated parameter space of the model become cosmologically allowed.
We also study the contribution to the DM relic density from direct and cascade
decays of the inflaton. Finally, we consider the case of a gravitino as dark
matter. We find strong bounds from overclosure and Big Bang Nucleosynthesis,
and derive lower limits on $T_R$ which depend on the gravitino mass and on the
nature of the lightest ordinary superpartner.
