We use idealized N-body simulations of equilibrium stellar disks embedded within course-grained dark matter haloes to study the effects of spurious collisional heating on disk structure and kinematics. Collisional heating drives a systematic increase in both the vertical and radial velocity dispersions of disk stars, and leads to an artificial increase in the thickness and size of disks; the effects are felt at all galacto-centric radii, and are not limited to the central regions of galaxies. We demonstrate that relaxation is driven primarily by the coarse-grained nature of simulated dark matter haloes, with bulges, stellar haloes and disk stars contributing little to disk heating. The integrated effects of collisional heating are determined primarily by the mass of dark matter particles (or equivalently by the number of particles at fixed halo mass), their local density and characteristic velocity, but are largely insensitive to the masses of stellar particles. This suggests that the effects of numerical relaxation on simulated galaxies can be reduced by increasing the mass resolution of the dark matter in cosmological simulations, with limited benefits from increasing the baryonic (or stellar) mass resolution. We provide a simple empirical model that accurately captures the effects of collisional heating on the vertical and radial velocity dispersions of disk stars, as well as on their scale heights. We use the model to assess the extent to which spurious collisional relaxation may have affected the structure of simulated galaxy disks. For example, we find that dark matter haloes resolved with fewer than $approx 10^6$ particles will collisionally heat stars near the stellar half-mass radius such that their vertical velocity dispersion increases by more than 10 per cent of the halos virial velocity in approximately one Hubble time.
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