The governing equations for fully developed laminar flow and heat transfer in the thermal entrance region of circular curved tubes are solved numerically for power law fluids. Detailed descriptions of the secondary velocity profiles and temperature profiles as a function of Dean number, Prandtl number and power law index are provided to elucidate the significant role of secondary convection. Results for friction factors, asymptotic Nusselt numbers and Nusselt numbers in the thermal entrance region are computed and compared with the published experimental and theoretical results for Newtonian and power law fluids. Satisfactory agreement is found. For a given Prandtl and Dean number the Nusselt number increases with increases in power law index and the thermal entrance length is found to be shortened for dilatant fluids in comparison with the pseudoplastic fluids.