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We discuss observations of CII*/CII ratios and cooling rates due to[CII]$\,$158$\mu$m emission in high-redshift intervening damped Lyman-$\alpha$systems towards quasars. We show that the observed bimodality in the CIIcooling rates actually reflects a bimodality in the CII*/CII-metallicity planethat can be naturally explained by phase segregation of the neutral medium,without invoking differences in star-formation scenarios. Assuming realisticdistributions of the physical parameters to calculate the phase diagrams, wealso reproduce qualitatively the metallicity dependence of this bimodality. Weemphasize that high-z DLAs mostly probe low-metallicity gas ($Z\lesssim 0.1Z_{\odot}$), where heating is dominated by cosmic rays (and/or turbulence), andnot by photoelectric heating. Therefore even if the gas of DLA is predominantlycold (where the cooling is dominated by [CII]), the excitation of CII can beused to derive the cosmic ray ionization rate (and/or turbulent heating), butnot the UV field, as was previously considered. Alternatively, if the gas inDLA is predominantly warm, CII*/CII can be used to constrain its numberdensity. Finally, we also discuss the importance of the ionized medium, which,if also present along the line of sight, can significantly increase the averageCII*/CII ratio.

CII*/CII ratio in high-redshift DLAs: ISM phase separation drives the observed bimodality of [CII] cooling rates