Surfaces in the engineering systems are usually not regarded as hydraulically smooth but have roughness, which considerably affects heat and momentum transfer particularly in high Reynolds number turbulent flows. It is thus crucial to accurately predict the effects of the wall roughness on turbulent heat and momentum transfer. In this study, we performed direct numerical simulations (DNSs) of turbulent heat transfer over three-dimensional sinusoidal rough surfaces to discuss the scaling of turbulent heat transfer over rough surfaces. Particular attention was paid to the effect of wavelengths of surface undulations on turbulent heat transfer. Accordingly, we performed a series of DNSs at different friction Reynolds numbers of 180, 300, and 600 for three-dimensional sinusoidal surfaces in which the streamwise and spanwise wavelengths were systematically varied while the roughness height was fixed. For the numerical method, we utilized the double distribution-function lattice Boltzmann method, which consists of the D3Q27 multiple-relaxation-time lattice Boltzmann method and the D3Q19 regularized Bhatnagar-Gross-Krook lattice Boltzmann method. We considered an incompressible fluid with passive scalar of the Prandtl number of 0.7. To quantify the effects of the wall roughness on heat and moment transfer, the temperature and velocity roughness functions are introduced, respectively. The roughness functions are defined as the downward shifts in the logarithmic profiles with respect to the smooth wall profiles. It is found that the velocity roughness function in the fully-rough regime is expressed as a function of the equivalent sand grain roughness solely irrespective of the wavelengths, whereas the wavelengths significantly affect the scaling of the temperature roughness function. Analysis of the physical mechanisms for the temperature roughness function suggests that the dominant mechanism that increases the temperature roughness function is the wall heat transfer term, which has a direct connection to the slope of surface undulations. To account for this effect, we propose the predictive correlation which incorporates the effective slope of surface undulations, and it is confirmed that the effective slop is the one of the promising candidate to improve predictive correlation for the temperature roughness function.