  We have analyzed the soft X-ray emission in a wide area of the Sculptor
supercluster by using overlapping ROSAT PSPC pointings. After subtraction of
the point sources we have found evidence for extended, diffuse soft X-ray
emission. We have investigated the nature of such extended emission through the
cross-correlation with the density of galaxies as inferred from the Muenster
Redshift Survey. In particular we have analyzed the correlation as a function
of the temperature of the X-ray emitting gas. We have found a significant
correlation of the galaxy distribution only with the softest X-ray emission
(0.1--0.3 keV) and only for gas temperatures kT < 0.5 keV. We have excluded
that this soft X-ray diffuse emission, and its correlation with the galaxy
distribution, is significantly contributed by unresolved AGN, group of galaxies
or individual galaxies. The most likely explanation is that the soft, diffuse
X-ray emission is tracing Warm-Hot Intergalactic Medium, with temperatures
below 0.5 keV, associated with the large-scale structures in the Sculptor
supercluster.
