Measurements of the kinetic temperature from the H₂ rotational excited states as a function of total H₂ column density (top) and metallicity (bottom). Red squares represent the GRBs from this work, where the arrows mark the upper limits on T_kin derived from T₁₂ (see text). The small blue diamond symbols denote quasar DLAs from the sample studied by Srianand et al. (2005), where large blue dots represent the same ES-DLAs shown in Fig. 10. The gray-shaded diamond symbols in the top panel again show selected sightlines through diffuse and translucent molecular clouds in the Milky Way (from Burgh et al. 2010). In the bottom panel, only the strongest DLAs with N(H I) > 10^21.7 cm⁻² are shown. The gray-shaded diamond symbols here represent the mean T_kin for Galactic diffuse and translucent molecular clouds (with error bars denoting the standard deviation), arbitrarily placed at solar metallicities.