  It was recently pointed out that semi-annihilating dark matter (DM) may
experience a novel temperature evolution dubbed as self-heating. Exothermic
semi-annihilation converts the DM mass to the kinetic energy. This yields a
unique DM temperature evolution, $T_{\chi} \propto 1 / a$, in contrast to $
T_{\chi} \propto 1 / a^{2}$ for free-streaming non-relativistic particles.
Self-heating continues as long as self-scattering sufficiently redistributes
the energy of DM particles. In this paper, we study the evolution of
cosmological perturbations in self-heating DM. We find that sub-GeV
self-heating DM leaves a cutoff on the subgalactic scale of the matter power
spectrum when the self-scattering cross section is $\sigma_{\rm self} /
m_{\chi} \sim {\cal O} (1) \,{\rm cm}^{2} /{\rm g}$. Then we present a particle
physics realization of the self-heating DM scenario. The model is based on
recently proposed strongly interacting massive particles with pion-like
particles in a QCD-like sector. Pion-like particles semi-annihilate into an
axion-like particle, which is thermalized with dark radiation. The dark
radiation temperature is smaller than the standard model temperature, evading
the constraint from the effective number of neutrino degrees of freedom. It is
easily realized when the dark sector is populated from the standard model
sector through a small coupling.
