  Asymmetric dark matter (ADM) that is captured in stars can act as an
efficient conductor of heat. Small ADM-induced changes in a star's temperature
gradient are known to alter neutrino fluxes and asteroseismological signatures,
erase convective cores and modify a star's main sequence lifetime. The Sun's
proximity to us makes it an ideal laboratory for studying these effects.
However, the two formalisms commonly used to parametrize such heat transport
were developed over 30 years ago, and calibrated with a single set of
simulations. What's more, both are based on assumptions that break down at the
Knudsen transition, where heat transport is maximized. We construct a Monte
Carlo simulation to exactly solve the Boltzmann collision equation, determining
the steady-state distribution and luminosity carried in stars by ADM with cross
sections that depend on velocity and momentum. We find that, although the
established (Gould and Raffelt) formalism based on local thermal equilibrium
does well for constant cross sections, the isothermal (Spergel and Press)
method actually performs better across all models with a simple, universal
rescaling function. Based on simulation results, we provide recommendations on
the parametrization of DM heat transport in stellar evolution models.
