The heating and cooling of the interstellar medium allow the gas in the ISM to coexist at very different temperatures in thermal pressure equilibrium. The heating cannot be directly determined, but the cooling can be inferred from observations of C II*, which is an important coolant in different environments. The amount of cooling can be measured through either the intensity of the 157.7 micron [C II] emission line or the C II* absorption lines at 1037.018 AA and 1335.708 AA, observable with FUSE and HST/STIS, respectively. We present the results of a survey of these far-UV absorption lines in 43 objects situated at |b|>30. We derive the cooling rates and analyze the ionization structure, the depletion, and metallicity content from the column densities of C II*, S II, P II, Fe II, and H I 21-cm emission for the low-, intermediate-, and high-velocity clouds (LVCs, IVCs, and HVCs) along the different sightlines. Based on the depletion and the ionization structure, the LVCs, IVCs, and HVCs consist mostly of warm neutral and ionized clouds. For the LVCs, the mean cooling rate in erg,s^{-1} per H atom is -25.70^{+0.19}_{-0.36} dex. The corresponding total Galactic C II luminosity in the 157.7 micron emission line is L~2.6x10^7 L_sun. Combining N(C II*) with the intensity of H$alpha$ emission, we derive that ~50% of the C II* radiative cooling comes from the warm ionized medium (WIM). The large dispersion in the cooling rates is certainly due to a combination of differences in the ionization fraction, in the dust-to-gas fraction, and physical conditions between sightlines. For the IVC IV Arch at z~1 kpc we find that on average the cooling is a factor 2 lower than in the LVCs that probe gas at lower z. For an HVC (Complex C, at z > 6 kpc) we find the much lower rate of -26.99^{+0.21}_{-0.53} dex. [Abridged]
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