ABSTRACT Warps are observed in a large fraction of disc galaxies, and can be due to a large number of different processes. Some of these processes might also cause vertical heating and flaring. Using a sample of galaxies simulated in their cosmological context, we study the connection between warping and disc heating. We analyse the vertical stellar density structure within warped stellar discs, and monitor the evolution of the scale heights of the mono-age populations and the geometrical thin and thick disc during the warp’s lifetime. We also compare the overall thickness and the vertical velocity dispersion in the disc before and after the warp. We find that for warps made of pre-existing stellar particles shifted off-plane, the scale heights do not change within the disc’s warped region: discs bend rigidly. For warps made of off-plane new stellar material (either born in situ or accreted), the warped region of the disc is not well described by a double sech2 density profile. Yet, once the warp is gone, the thin and thick disc structure is recovered, with their scale heights following the same trends as in the region that was never warped. Finally, we find that the overall thickness and vertical velocity dispersion do not increase during a warp, regardless of the warp’s origin. This holds even for warps triggered by interactions with satellites, which cause disc heating but before the warp forms. Our findings suggest that the vertical structure of galaxies does not hold any memory of past warps.