A theoretical study of turbulent channel flows was conducted in order to investigate the relationship between the heat-transfer enhancement and the increase in drag by rough surfaces using time-space averaged momentum and energy equations. The results confirmed that the efficiency of heat-transfer surfaces is in general less than unity when the molecular Prandtl number of the working fluid is less than the turbulent Prandtl number. When the molecular Prandtl number is greater than the turbulent Prandtl number, on the other hand, it was shown that the efficiency could be greater than unity as long as the surface roughness is transitional. It is suggested that the breakdown of the Reynolds analogy being experimentally observed for the riblet surface seems to be due to the inhomogeneity of the heat flux over the micro-grooves at the initial stage of thermal boundary-layer development.