Electronic structures of the transition-metal monosilicides FeSi and CoSi have been studied by x-ray photoelectron spectroscopy (XPS) and bremsstrahlung isochromat spectroscopy (BIS) as a function of temperature. The XPS valence-band spectra and the BIS conduction-band spectra at low temperature (\ensuremath{\sim}120 K) are in qualitative agreement with the calculated densities of states of MnSi and the rigid-band picture, except that the overall width of the metal 3d-derived states becomes narrower as the number of d electrons is increased. The valence-band spectra of FeSi and CoSi show an unusually large difference as the temperature is raised to \ensuremath{\sim}700 K, which cannot be readily explained by existing models of phonon broadening. The Fe 3s core-level spectra of FeSi show no detectable satellites due to exchange interaction between the 3d electrons and the 3s core hole at either low or high temperature, giving no indication of the temperature-induced local magnetic moments that were recently suggested from the spin-fluctuation theory of itinerant magnetism.