Doppler broadening of neutron cross sections is described under the combined influence of temperature and boundary motion. The effective cross section is explicitly presented for the two cases of a constant speed, isotropic boundary motion (which is identical to the condition of an isotropic neutron flux), and also a constant speed, monodirectional boundary motion. The functional relations interconnecting the effective cross section at different temperatures and boundary motion velocities are pointed out. The results of numerical calculations are also presented.