  The capture of dark matter, and its subsequent annihilation, can heat old,
isolated neutron stars. In order for kinetic heating to be achieved, the
captured dark matter must undergo sufficient scattering to deposit its kinetic
energy in the star. We find that this energy deposit typically occurs quickly,
for most of the relevant parameter space. In order for appreciable annihilation
heating to also be achieved, the dark matter must reach a state of
capture-annihilation equilibrium in the star. We show that this can be
fulfilled for all types of dark matter - baryon interactions. This includes
cases where the scattering or annihilation cross sections are momentum or
velocity suppressed in the non-relativistic limit. Importantly, we find that
capture-annihilation equilibrium, and hence maximal annihilation heating, can
be achieved without complete thermalization of the captured dark matter. For
scattering cross sections that saturate the capture rate, we find that
capture-annihilation equilibrium is typically reached on a timescale of less
than $1$ year for vector interactions and $10^4$ years for scalar interactions.
