  Context. A significant fraction of the predicted baryons remains undetected
in the local universe. We adopted the common assumption that a large fraction
of the missing baryons corresponds to the hot (log T(K) = 5.5-7) phase of the
Warm Hot Intergalactic Medium (WHIM). We base our missing baryons search on the
scenario whereby the WHIM has been heated up via accretion shocks and galactic
outflows, and is concentrated towards the filaments of the Cosmic Web.
  Aims. Our aim is to improve the observational search of the poorly detected
hot WHIM.
  Methods. We detect the filamentary structure within the EAGLE simulation by
applying the Bisous formalism to the galaxy distribution. In addition, we use
the MMF/NEXUS+ classification of the large scale environment of the dark matter
component in EAGLE. We then study the spatio-thermal distribution of the hot
baryons within the extracted filaments.
  Results. While the filaments occupy only 5% of the full simulation volume,
the diffuse hot intergalactic medium in filaments amounts to 23% $-$ 25% of the
total baryon budget, or 79% $-$ 87% of all the hot WHIM. The most optimal
filament sample, with a missing baryon mass fraction of 82%, is obtained by
selecting Bisous filaments with a high galaxy luminosity density. For these
filaments we derived analytic formulae for the radial gas density and
temperature profiles, consistent with recent Planck SZ and CMB lensing
observations within the central $r$~ 1 Mpc.
  Conclusions. Results from EAGLE suggest that the missing baryons are strongly
concentrated towards the filament axes. Since the filament finding methods used
here are applicable to galaxy surveys, a large fraction of the missing baryons
can be localised by focusing the observational efforts on the central 1 Mpc
regions of the filaments. Moreover, focusing on high galaxy luminosity density
regions will optimise the observational signal.
