Conductive heat transport across an isothermal three-dimensional irregular surface into a semi-infinite conductive medium and heat transport across the interface between two semi-infinite conductive media are considered by asymptotic and numerical methods. The temperature profile far from the surface or interface varies in a linear manner with respect to distance normal to the mean position of the surface or interface, and is displaced by a constant with respect to the linear profile corresponding to the flat geometry. The displacement constant amounts to a macroscopic temperature drop or discontinuity that depends on the geometry of the irregularities and on the media conductivities. An asymptotic expansion for the jump is derived by the method of domain perturbation for small-amplitude, doubly-periodic corrugations, and an integral formulation is developed for finite-amplitude corrugations. Numerical results based on the boundary element method for three-dimensional wavy corrugations with square or hexagonal pattern show that the asymptotic results are accurate when the ratio of the vertical span to the wavelength of the corrugations is less than roughly 0.5. Illustrations of the flux distribution over the corrugated surfaces show explicitly a considerable enhancement or reduction at the crests or troughs, even for moderate-amplitude irregularities.