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For the Warm Dark Matter (WDM) candidates the momentum distribution ofparticles becomes important, since it can be probed with observations ofLyman-$\alpha$ forest structures and confronted with coarse grained phase spacedensity in galaxy clusters. We recall the calculation bt Kaplinghat (2005) ofthe spectrum in case of dark matter non-thermal production in decays of heavyparticles emphasizing on the inherent applicability conditions, which arerather restrictive and sometimes ignored in literature. Cold part of thespectrum requires special care when WDM is considered.

On the applicability of approximations used in calculation of spectrum of Dark Matter particles produced in particle decays