  In this third paper of the series, we investigate the effects of warm dark
matter with a particle mass of $m_\mathrm{WDM}=3\,\mathrm{keV}$ on the smallest
galaxies in our Universe. We present a sample of 21 hydrodynamical cosmological
simulations of dwarf galaxies and 20 simulations of satellite-host galaxy
interaction that we performed both in a Cold Dark Matter (CDM) and Warm Dark
Matter (WDM) scenario. In the WDM simulations, we observe a higher critical
mass for the onset of star formation. Structure growth is delayed in WDM, as a
result WDM haloes have a stellar population on average two Gyrs younger than
their CDM counterparts. Nevertheless, despite this delayed star formation, CDM
and WDM galaxies are both able to reproduce the observed scaling relations for
velocity dispersion, stellar mass, size, and metallicity at $z=0$. WDM
satellite haloes in a Milky Way mass host are more susceptible to tidal
stripping due to their lower concentrations, but their galaxies can even
survive longer than the CDM counterparts if they live in a dark matter halo
with a steeper central slope. In agreement with our previous CDM satellite
study we observe a steepening of the WDM satellites' central dark matter
density slope due to stripping. The difference in the average stellar age for
satellite galaxies, between CDM and WDM, could be used in the future for
disentangling these two models.
