Corrugated walls are widely used as passive devices for heat and mass transfer enhancement; they are most effective when operated at transitional and turbulent Reynolds numbers. In the present study, direct numerical simulation is used to investigate the unsteady forced convection in sinusoidal, symmetric wavy channels. A novel numerical method is employed for the simulations; it is meant for fully developed flows in periodic ducts of prescribed wall temperature. The algorithm is free of iterative procedures; it accounts for the effects of streamwise diffusion and can be used for unsteady problems. Results of two simulations in the transitional regime for Reynolds numbers based on average duct height and average velocity of $Re=481$ and $Re=872$ are reported. Time averaged and instantaneous velocity and temperature fields together with second-order statistics are interpreted in order to describe the mechanism associated with heat transfer augmentation. Heat flux distributions locate the most active areas in heat transfer and reveal the effects of convective mixing. Slanted traveling waves of high temperature are identified; peak values of Nusselt number are attained when the high-temperature fluid of the waves reaches the converging walls.