New Constraints on "Cool" Dark Matter

It has been suggested that a sterile neutrino \nu_s which mixes with standard neutrinos can form nonthermal ``cool'' Dark Matter if its mass and mixing angle fall in the ranges 0.1 keV \lsim m_s \lsim 10 keV and 10^{-10} \lsim \sin^2 \theta \lsim 10^{-4}, respectively. We point out that the required mixing makes these heavy neutrinos unstable. The dominant decay mode is into three light neutrinos, but the most stringent constraint comes from the non-observation of radiative decays into a single light neutrino and a photon. Moreover, we point out that the density of thermal relics of such \nu_{s}'s would be too high, unless the reheating temperature after inflation was below \sim 10 GeV.