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We calculate the production rate of singlet fermions from the decay ofneutral or charged scalar fields in a hot plasma. We find that there areconsiderable thermal corrections when the temperature of the plasma exceeds themass of the decaying scalar. We give analytic expressions for thetemperature-corrected production rates in the regime where the decay productsare relativistic. We also study the regime of non-relativistic decay productsnumerically. Our results can be used to determine the abundance and momentumdistribution of Dark Matter particles produced in scalar decays. The inclusionof thermal corrections helps to improve predictions for the free streaming ofthe Dark Matter particles, which is crucial to test the compatibility of agiven model with cosmic structure formation. With some modifications, ourresults may be generalised to the production of other Dark Matter candidates inscalar decays.

Sterile neutrino Dark Matter production from scalar decay in a thermal bath