ABSTRACT We discuss observations of C ii*/C ii ratios and cooling rates due to [C ii] 158μm emission in high-redshift intervening damped Lyman-α (DLA) systems towards quasars. We show that the observed bimodality in the C ii cooling rates actually reflects a bimodality in the C ii*/C ii−metallicity plane that can be naturally explained by phase segregation of the neutral medium, without invoking differences in star-formation scenarios. Assuming realistic distributions of the physical parameters to calculate the phase diagrams, we also reproduce qualitatively the metallicity dependence of this bimodality. We emphasize that high-z DLAs mostly probe low-metallicity gas ($Z\lesssim 0.1 \, \mathrm{Z}_{\odot }$), where heating is dominated by cosmic rays (and/or turbulence), and not by photoelectric heating. Therefore, even if the gas of DLA is predominantly cold (where the cooling is dominated by [C ii]), the excitation of C ii can be used to derive the cosmic ray ionization rate (and/or turbulent heating), but not the UV field, as was previously considered. Alternatively, if the gas in DLA is predominantly warm, C ii*/C ii can be used to constrain its number density. Finally, we also discuss the importance of the ionized medium, which, if also present along the line of sight, can significantly increase the average C ii*/C ii ratio.