  Hydrodynamical simulations indicate that substantial fraction of baryons in
the Universe remains in a diffuse component - Warm-Hot Intergalactic Medium
(WHIM). To determine physical properties (spatial distribution, temperature and
density) of the WHIM, spatial structure of the soft extended X-ray emission
surrounding field galaxies is carefully investigated using the XMM-Newton
EPIC/MOS observations. Angular correlations between the galaxy distribution and
the soft X-ray background extending over several arcmin are determined. The
correlations at large scales result from the clustering of galaxies. At small
scales (below ~2 arcmin) the excess of the soft flux is interpreted as the
genuine emission from halos of the WHIM surrounding individual galaxies. Bulk
parameters of the average WHIM halos associated with galaxies in the sample are
estimated. Typical halo has a characteristic radius of ~0.3 Mpc and a mass of 4
- 7 x 10^11 M_sun. The average density of the WHIM in the local universe
amounts to 7 - 11 x 10^{-32} g cm^{-3} (Omega_WHIM = 0.7 - 1.2 %). Observations
of the X-ray WHIM emission are in good agreement with the numerical
simulations, but accuracy of the observational material is insufficient to
constrain the theory of WHIM. A series of deep observations of a moderately
numerous sample of low redshift galaxies with high resolution instruments of
Chandra would significantly improve our estimates of the WHIM parameters.
