  We study properties of hadrons in the O(4) linear $\sigma$ model, where we
take into account fluctuations of mesons around their mean field values using
the Gaussian functional (GF) method. In the GF method we calculate dressed
$\sigma$ and $\pi$ masses, where we include the effect of fluctuations of
mesons to find a better ground state wave function than the mean field
approximation. Then we solve the Bethe-Salpeter equations and calculate
physical $\sigma$ and $\pi$ masses. We recover the Nambu-Goldstone theorem for
the physical pion mass to be zero in the chiral limit. The $\sigma$ meson is a
strongly correlated meson-meson state, and has a 4 quark structure. We
calculate $\sigma$ and $\pi$ masses as functions of temperature for the two
cases of chiral limit and explicit chiral symmetry breaking. We get similar
behaviors for the $\sigma$ and $\pi$ masses as the case of the mean field
approximation, but the coupling constants are much larger than the values of
the case of the mean field approximation.
