  We calculate the pressure of the interacting pion gas using the
Beth-Uhlenbeck approach to the relativistic virial expansion with Breit-Wigner
phase shifts for the $\sigma$- and $\varrho$- meson resonances. The repulsive
phase shift $\delta^2_0$ is taken from quark interchange model of Barnes and
Swanson [Phys. Rev. D 46 (1992) 131] in very good agreement with experimental
data. In this work we show that the cancellation of the attractive (I = 0) and
repulsive (I = 2) isospin channel contributions to the scalar $\pi-\pi$
interaction in the low-energy region that is known for the vacuum phase shifts,
takes place also at finite temperature. This happens despite the strong medium
dependence of these phase shifts that enters our model by the temperature
dependence of the $\sigma$- meson and constituent quark masses because for
these masses the relation $m_\sigma(T) \approx 2 m_q (T)$ holds and the
scattering length approximation is valid as long as the strong decay channel
$\sigma \to \pi \pi$ is open. Exploiting the Nambu--Jona-Lasinio model for
describing the dynamical breaking of chiral symmetry in the vacuum and its
restoration at finite temperature, we justify with our approach that the
$\sigma$-meson should be absent from the hadron resonance gas description at
low temperatures because the above cancellation holds. However, since this
cancellation breaks down in the vicinity of the hadronization transition, where
due to chiral symmetry restoration the decay channel $\sigma \to \pi \pi$
closes and the $\sigma$- meson becomes a good resonance, the latter should be
included into the statistical model description of chemical freeze-out in
heavy-ion collisions.
