We present Suzaku spectra of X-ray emission in the fields just off the LMC X–3 sight line . O VII , O VIII , and Ne IX emission lines are clearly detected , suggesting the presence of an optically thin thermal plasma with an average temperature of 2.4 \times 10 ^ { 6 } K. This temperature is significantly higher than that inferred from existing X-ray absorption line data obtained with Chandra grating observations of LMC X–3 , strongly suggesting that the gas is not isothermal . We then jointly analyze these data to characterize the spatial and temperature distributions of the gas . Assuming a vertical exponential Galactic disk model , we estimate the gas temperature and density at the Galactic plane and their scale heights as 3.6 ( 2.9 , 4.7 ) \times 10 ^ { 6 } K and 1.4 ( 0.3 , 3.4 ) \times 10 ^ { -3 } ~ { } { cm ^ { -3 } } and 1.4 ( 0.2 , 5.2 ) kpc and 2.8 ( 1.0 , 6.4 ) kpc , respectively . This characterization can account for all the O VI line absorption , as observed in a FUSE spectrum of LMC X–3 , but only predicts less than one tenth of the O VI line emission intensity typically detected at high Galactic latitudes . The bulk of the O VI emission most likely arises at interfaces between cool and hot gases .