The rates of heat transfer for flow through a periodic array of wavy passages are studied with an accurate numerical scheme. The flow was observed to be steady until Re around 180 after which self-sustained oscillatory flow was observed. The self-sustained oscillations lead to the destabilization of laminar thermal boundary layers, replenish the near-wall fluid with the fluid in the core region, and thus provide a natural mechanism of heat and mass transfer enhancement. In the steady-flow regime, the average Nusselt numbers for the wavy wall channel were only slightly larger than those for a parallel-plate channel. On the other hand, in the transitional-flow regime, the enhancement of heal transfer was about a factor of 2.5. Friction factors for the wavy channel were about twice those for the parallel-plate channel in the steady-flow region, and remained almost constant in the transitional regime.