We present all-sky maps of two major far-ultraviolet cooling lines, C IV and O VI, of highly ionized gas to investigate the nature of the transition-temperature gas. From the extinction-corrected line intensities of C IV and O VI, we calculated the gas temperature and the emission measure of the transition-temperature gas assuming isothermal plasma in the collisional ionization equilibrium. The gas temperature was found to be more or less uniform throughout the Galaxy with a value of (1.89 +/- 0.06) x 10(5) K. The emission measure of the transition-temperature gas is described well by a disk-like model in which the scale height of the electron density is z(0) = 6(-2)(+3) kpc. The total mass of the transition-temperature gas is estimated to be approximately 6.4(-2.8)(+5.2) x 10(9)M(circle dot). We also calculated the volume-filling fraction of the transition-temperature gas, which was estimated to be f = 0.26 +/- 0.09, and it varies from f similar to 0.37 in the inner Galaxy to f similar to 0.18 in the outer Galaxy. The spatial distribution of C IV and O VI cannot be explained by a simple supernova remnant model or a three-phase model. The combined effects of supernova remnants and turbulent mixing layers can explain the intensity ratio of C IV and O VI. Thermal conduction front models and high-velocity cloud models are also consistent with our observation.