  Small angular scale structure of the soft X-ray background correlated with
the galaxy distribution is investigated. An extensive data sample from the
ROSAT and XMM-Newton archives are used. Excess emission below 1 keV extending
up to at least 1.5 Mpc around galaxies is detected. The relative amplitude of
the excess emission in the 0.3-0.5 keV band amounts to 1.3+/-0.2 % of the total
background flux. A steep spectrum of the emission at higher energies is
indicated by a conspicuous decline of the signal above 1 keV. The XMM-Newton
EPIC/MOS data covering wider energy range than the ROSAT PSPC are consistent
with a thermal bremsstrahlung spectrum with k}T < 0.5 keV. This value is
consistent with temperatures of the Warm-Hot Intergalactic Medium derived by
several groups from hydrodynamic simulations. Correlation analysis allows for
estimate of the average excess emission associated with galaxies but the data
are insufficient to constrain physical parameters of the WHIM and to determine
the contribution of WHIM to the total baryonic mass density.
