Heat flux between river water and riverbed contributes significantly to river water heat content and river temperature, especially in shallow rivers. A numerical model of heat conduction in a riverbed was verified with detailed temperatures measurements in a riverbed. Three different methods, the heat budget method, the gradient method, and an inverse method, were used alternatively for the estimation of the riverbed heat flux. Propagation of uncertainty in the riverbed temperature model was studied using a vector state space perturbation method. Output uncertainty was estimated by random perturbations of the effective thermal conductivity from the main value. The coefficient of variation of effective thermal conductivity was 0.1. Temperatures and heat fluxes in the riverbed were affected by the uncertain thermal conductivity. ¿ American Geophysical Union 1994