We calculate the phonon, electron, and magnon temperature profiles in yttrium iron garnet/platinum bilayers by diffusive theory with appropriate boundary conditions, in particular taking into account interfacial thermal resistances. Our calculations show that in thin film hybrids, the interface magnetic heat conductance qualitatively affects the magnon temperature. Based on published material parameters we assess the degree of nonequilibrium at the yttrium iron garnet/platinum interface. The magnitude of the spin Seebeck effect derived from this approach compares well with experimental results for the longitudinal spin Seebeck effect. Additionally, we address the temperature profiles in the transverse spin Seebeck effect.