  Cosmological simulations of the $\Lambda$CDM model suggest that the dark
matter halos of dwarf galaxies are denser in their center than what
observational data of such galaxies imply. In this letter, we propose a novel
solution to this problem by invoking a certain class of dark matter
self-heating processes. As we will argue, such processes lead to the formation
of dark matter cores at late times by considerably reducing the inner mass
density of dwarf-sized halos. For deriving concrete results, we focus on
semi-annihilating dark matter scenarios and model the inner region of dark
matter halos as a gravothermal fluid. An important aspect of this new solution
is that the semi-annihilation effects are much more prominent in dwarf-sized
halos than in the more massive halos that host galaxies and clusters, even if
the corresponding cross sections are the same. Furthermore, the preferred
parameter space for solving the small-scale problem suggests a thermal dark
matter candidate with a mass below the GeV scale, which can be probed in dark
matter direct and indirect detection experiments.
