  The massive scalar field with $\lambda\varphi^4$ interaction placed in
$(3+1)$ dimensional box is considered. The sizes of the box are $V\times \beta$
$(V=L^3$ is the volume, $T=1/\beta$ is the temperature). The free energy is
evaluated up to the 2nd order of $PT$. The averaging on the vacuum fluctuations
is separated from the averaging on the thermal fluctuations explicitly. As
result the free-energy is expressed through the scattering amplitudes. We find
that in 3-loop approximation the expression for free energy coincides with the
ansatz of Bernstein, Dashen, Ma suggested on the base of $S$-matrix formulation
of statistical mechanics. The obtained expressions are generalized for higher
order of $PT$.
