  Every dark matter halo and subhalo is expected to have a prompt $\rho\propto
r^{-1.5}$ central density cusp, which is a relic of its condensation out of the
smooth mass distribution of the early universe. The sizes of these prompt cusps
are linked to the scales of the peaks in the initial density field from which
they formed. In warm dark matter (WDM) models, the smoothing scale set by free
streaming of the dark matter can result in prompt cusps with masses of order
$10^7$ M$_\odot$. We show that WDM models with particle masses ranging from 2
to 6 keV predict prompt cusps that could detectably alter the observed
kinematics of Local Group dwarf galaxies. Thus, prompt cusps present a viable
new probe of WDM. A prompt cusp's properties are highly sensitive to when it
formed, so prospects can be improved with a better understanding of when the
haloes of the Local Group dwarfs originally formed. Tidal stripping can also
affect prompt cusps, so constraints on satellite galaxy orbits can further
tighten WDM inferences.
