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 × 106 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) × 106 K and 1.4(0.3, 3.4) × 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 Far Ultraviolet Spectroscopy Explorer 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.