In this paper, we present a formal Fourier analysis (FA) of Picard iteration for the coupled neutronics/thermal hydraulics (N/TH) problem and derive theoretical predictions for the spectral radius of Picard iteration for such coupled calculations as a function of the temperature difference between the fuel and coolant, temperature coefficients of cross sections (i.e., Doppler feedback), scattering ratio, and core height. An optimal underrelaxation factor is also derived based on the Fourier analysis.