The effect of three-dimensional hydrodynamics on the enhancement of steady, laminar heat transfer in corrugated channels is studied using a combination of analytical and numerical techniques. Reynolds numbers are considered in the range of 0 < Re < 250 to avoid unsteady flow. Two-dimensional sinusoidal corrugations with flow perpendicular to the corrugations is taken as the base. The heat transfer is higher than for flat plates due to the presence of recirculation zones; there is increased advection near each stagnation point which, when combined with the asymmetry of the flow in the downstream direction, leads to a larger area-averaged heat transfer coefficient. In the three-dimensional case the corrugations are sinusoidal in two orthogonal directions. A small mean flow in the transverse direction leads to an increase in the heat transfer by allowing particles to cross between the recirculation zones and the main flow. As the transverse flow becomes stronger, the recirculation is destroyed and there is a corresponding decrease in heat transfer.