  Three observational constraints can be placed on a warm-hot intergalactic
medium (WHIM) using \rosat PSPC pointed and survey data, the emission strength,
the energy spectrum, and the fluctuation spectrum. The upper limit to the
emission strength of the WHIM is 7.5 +/- 1.0 keV s^-1 cm^-2 sr^-1 keV^-1 in the
3/4 keV band, an unknown portion of which value may be due to our own Galactic
halo. The spectral shape of the WHIM emission can be described as thermal
emission with log T=6.42, although the true spectrum is more likely to come
from a range of temperatures. The values of emission strength and spectral
shape are in reasonable agreement with hydrodynamical cosmological models. The
autocorrelation function in the 0.44 keV < E < 1.21 keV band range, w(theta),
for the extragalactic soft X-ray background (SXRB) which includes both the WHIM
and contributions due to point sources, is less than about 0.002 for 10
arcminutes < theta < 20 arcminutes in the 3/4 keV band. This value is lower
than the Croft et al. (2000) cosmological model by a factor of about 5, but is
still not inconsistent with cosmological models. It is also found that the
normalization of the extragalactic power law component of the soft X-ray
background spectrum must be 9.5 +/- 0.9 keV s^-1 cm^-2 sr^-1 keV^-1 to be
consistent with the ROSAT All-Sky Survey.
