  Dissipative dark matter, such as mirror dark matter and related hidden sector
dark matter candidates, requires an energy source to stabilize dark matter
halos in spiral galaxies. It has been proposed previously that supernovae could
be the source of this energy. Recently, it has been argued that this mechanism
might explain two galactic scaling relations inferred from observations of
spiral galaxies. One of which is that $\rho_0 r_0$ is roughly constant, and
another relates the galactic luminosity to $r_0$. [$\rho_0$ is the dark matter
central density and $r_0$ is the core radius.] Here we derive equations for the
heating of the halo via supernova energy, and the cooling of the halo via
thermal bremsstrahlung. These equations are numerically solved to obtain
constraints on the $\rho_0, \ r_0$ parameters appropriate for spiral galaxies.
These constraints are in remarkable agreement with the aforementioned scaling
relations.
