Three observational constraints can be placed on a warm-hot intergalactic m
edium (WHIM) using ROSAT Position Sensitive Proportional Counter pointed ob
servations and survey data: the emission strength, the energy spectrum, and
the fluctuation spectrum. The upper limit to the emission strength of the
WHIM is keV 7.5 +/- 1.0 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 sp
ectral shape of the WHIM emission can be described as thermal emission with
, although log T = 6.42 the true spectrum is more likely to come from a ran
ge of temperatures. The values of the emission strength and spectral shape
are in reasonable agreement with hydrodynamical cosmological models. The au
tocorrelation 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 the contributions due to point sources, is less than or similar t
o0.002 for in the 10' < <theta> < 20' in the 3/4 keV band. This value is lo
wer than the Croft et al. cosmological model by a factor of <similar to>5 b
ut is still not inconsistent with cosmological models. It is also found tha
t the normalization of the extragalactic power-law component of the SXRB sp
ectrum must be 9.5 +/- 0.0 keV s(-1) cm(-2) sr(-1) keV(-1) to be consistent
with the ROSAT All-Sky Survey.