Dozens of direct detection experiments around the world are searching for the small dark matter-nucleon interactions that would give us the first clue about the true nature of dark matter. If such interactions exist, they would also cause dark matter to become trapped inside stars. Because of their long mean free paths, these particles can act as an efficient source of heat conduction. In the Sun, this can affect neutrino fluxes and helioseismology. In other stars it can erase convective cores, change the available supply of hydrogen and alter stars' lifetimes and luminosity-temperature relationships. Such predictions are based on two approximate – and contradictory – solutions to a Boltzmann equation, which were first proposed in the 80s and validated by a few simulations more than 30 years ago. I will discuss an update to this story: we have built our own Monte Carlo simulation of heat transport by dark matter particles in stars for a variety of possible dark matter-nucleon interactions. I will show the first results of these simulations, which lead us to a surprising conclusion about how heat transport should be thought of in such environments.