  We investigate the effects of a K-mouflage modification of gravity on the
dynamics of clusters of galaxies. We extend the description of K-mouflage to
situations where the scalar field responsible for the modification of gravity
is coupled to a perfect fluid with pressure. We describe the coupled system at
both the background cosmology and cosmological perturbations levels, focusing
on cases where the pressure emanates from small-scale nonlinear physics. We
derive these properties in both the Einstein and Jordan frames, as these two
frames already differ by a few percents at the background level for K-mouflage
scenarios, and next compute cluster properties in the Jordan frame that is
better suited to these observations. Galaxy clusters are not screened by the
K-mouflage mechanism and therefore feel the modification of gravity in a
maximal way. This implies that the halo mass function deviates from
$\Lambda$-CDM by a factor of order one for masses $M\gtrsim 10^{14} \ h^{-1}
M_\odot$. We then consider the hydrostatic equilibrium of gases embedded in
galaxy clusters and the consequences of K-mouflage on the X-ray cluster
luminosity, the gas temperature, and the Sunyaev-Zel'dovich effect. We find
that the cluster temperature function, and more generally number counts, are
largely affected by K-mouflage, mainly due to the increased cluster abundance
in these models. Other scaling relations such as the mass-temperature and the
temperature-luminosity relations are only modified at the percent level due to
the constraints on K-mouflage from local Solar System tests.
