Temperature evolution of a gas element subject to radiative cooling and heating by collisions with dark matter particles for constant ﹩\sigma _{xp}﹩ (﹩a=0﹩) and ﹩V_{x}/ V_{p}=0.5﹩. The top, middle, and bottom panels correspond to initial temperatures of 16, 8, and 3 keV, respectively. Dashed and dotted curves are, respectively, for ﹩n_{p}=0.007﹩ and ﹩0.015\ \mathrm{cm}\,^{-3}﹩, at the initial time. The solid curve is obtained with radiative cooling only for ﹩n_{p}=0.007\ \mathrm{cm}\,^{-3}﹩. The labels on the dashed curve indicate ﹩\sigma _{xp}﹩ in units of ﹩10^{-25}( m_{x}/ m_{p}) \ \mathrm{cm}\,^{2}﹩.