We use idealized N-body simulations of equilibrium stellar discs embedded within course-grained dark matter (DM) haloes to study the effects of spurious collisional heating on disc structure and kinematics. Collisional heating artificially increases the vertical and radial velocity dispersions of disc stars, as well as the thickness and size of discs; the effects are felt at all galacto-centric radii. The integrated effects of collisional heating are determined by the mass of DM halo particles (or equivalently, by the number of particles at fixed halo mass), their local density and characteristic velocity dispersion, but are largely insensitive to the stellar particle mass. The effects can therefore be reduced by increasing the mass resolution of DM 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 spurious collisional heating on the structure and kinematics of simulated discs, and use it to assess the importance of disc heating for simulations of galaxy formation. We find that the majority of state-of-the-art zoom simulations, and a few of the highest-resolution, smallest-volume cosmological runs, are in principle able to resolve thin stellar discs in Milky Way-mass haloes, but most large-volume cosmological simulations cannot. For example, DM haloes resolved with fewer than ≈106 particles will collisionally heat stars near the stellar half-mass radius such that their vertical velocity dispersion increases by ≲ 10 per cent of the halo's virial velocity in approximately one Hubble time.