  We present Suzaku spectra of X-ray emission in the fields just off the LMC
X-3 sight line. OVII, OVIII, and NeIX emission lines are clearly detected,
suggesting the presence of an optically thin thermal plasma with an average
temperature of 2.4E6. 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)E6 K and 1.4(0.3, 3.4)E-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 \ovi line absorption, as observed in a FUSE spectrum of LMC
X-3, but only predicts less than one tenth of the OVI line emission intensity
typically detected at high Galactic latitudes. The bulk of the OVI emission
most likely arises at interfaces between cool and hot gases.
