We study the quantum dynamics of the center-of-mass momentum distribution for the populations of a cold gas with two-level system undergoing spontaneous decay and coupled to a Markovian thermal reservoir at arbitrary temperature. We derive the momentum-convolutionless coupled equations for momentum Fourier transform of the populations which can be easily solved numerically and analytically for a specific internal scheme and for zero-temperature cases. The time and momentum evolutions of the populations are obtained by inverse Fourier transform. The momentum spread and the center-of-mass entropy across one momentum dimension are computed and compared for different internal schemes, between zero-temperature and finite-temperature cases and between π and σ± transitions. For initial subrecoil momentum width, the σ± transition displays a two-peak feature. Our results well describe the momentum spread dynamics of cold gas in thermal radiation at early time and complement the results based on Fokker-Planck equation.