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We test the luminosity function of Milky Way satellites as a constraint for the nature of dark matter particles. We perform dissipationless high‐resolution  N ‐body simulations of the evolution of Galaxy‐sized halo in the standard cold dark matter model and in four warm dark matter (WDM) scenarios, with a different choice for the WDM particle mass   m  w  . We then combine the results of the numerical simulations with semi‐analytic models for galaxy formation, to infer the properties of the satellite population. Quite surprisingly, we find that even WDM models with relatively low   m  w   values (2–5 keV) are able to reproduce the observed abundance of ultra faint  ( M v   &lt; −9)  dwarf galaxies, as well as the observed relation between luminosity and mass within 300 pc. Our results suggest a lower limit of 1 keV for thermal WDM, in broad agreement with previous results from other astrophysical observations such as Lyman α forest and gravitational lensing.

How cold is dark matter? Constraints from Milky Way satellites