This describes an experimental technique to determine the average velocity of the thermal-neutron spectrum as a function of time in a pulsed-neutron experiment. The measurement of the average velocity as a function of time is used to determine two parameters: the time necessary to establish an asymptotic spectrum, and the average velocity of the asymptotic spectrum. The variation in the asymptotic average velocity with material buckling is described by a “spectral-shift coefficient” which is related to the diffusion-cooling coefficient. It was found necessary to wait 2 milliseconds for the establishment of an equilibrium spectrum in graphite, and 0.6 milliseconds in heavy water, and that these values are insensitive to the geometric buckling. Values of the spectral-shift coefficient are given and compared with theoretical estimates.