We present a unified analysis of the O vi absorption-lines seen in the disk and halo of the Milky Way , high velocity clouds , the Magellanic Clouds , starburst galaxies , and the intergalactic medium . We show that these disparate systems define a simple relationship between the O vi column density and absorption-line width that is independent of the Oxygen abundance over the range O/H \sim 10 % to twice solar . We show that this relation is exactly that predicted theoretically as a radiatively cooling flow of hot gas passes through the coronal temperature regime - independent of its density or metallicity ( for O/H \gtrsim 0.1 solar ) . Since most of the intergalactic O vi clouds obey this relation , we infer that they can not have metallicities less than a few percent solar . In order to be able to cool radiatively in less than a Hubble time , the intergalactic clouds must be smaller than \sim 1 Mpc in size . The implied global heating rate of the warm/hot IGM is consistent with available sources . We show that the cooling column densities for the O iv , O v , Ne v , and Ne vi ions are comparable to those seen in O vi . This is also true for the Li-like ions Ne viii , Mg x , and Si xii ( if the gas is cooling from T \gtrsim 10 ^ { 6 } K ) . All these ions have strong resonance lines in the extreme-ultraviolet spectral range , and would be accessible to FUSE at z \gtrsim 0.2 to 0.8 . We also show that the Li-like ions can be used to probe radiatively cooling gas at temperatures an order-of-magnitude higher than where their ionic fraction peaks . We calculate that the H-like ( He-like ) O , Ne , Mg , Si , and S ions have cooling columns of \sim 10 ^ { 17 } ( few \times 10 ^ { 16 } ) cm ^ { -2 } . The properties of the O vii , O viii , and Ne ix X-ray absorption-lines towards PKS 2155-304 may be consistent with a scenario of radiatively cooling gas in the Galactic disk or halo .