  The by now well-established scalar-isoscalar resonance $f_{0}(500)$ (the
$\sigma$ meson) seems potentially relevant in the evaluation of thermodynamic
quantities of a hadronic gas, since its mass is low. However, we recall that
its contribution to isospin-averaged observables is, to a surprising accuracy,
canceled by the repulsion from the pion-pion scalar-isotensor channel. As a
result, in practice one should not incorporate $f_0(500)$ in standard hadronic
resonance-gas models for studies of isospin averaged quantities. In our
analysis we use the formalism of the virial expansion, which allows one to
calculate the thermal properties of an interacting hadron gas in terms of
derivatives of the scattering phase shifts, hence in a model-independent way
directly from experimentally accessible quantities. A similar cancellation
mechanism occurs for the scalar kaonic interactions between the $I=1/2$ channel
(containing the alleged $K_{0}^{\ast}(800)$ or the $\kappa$ meson) and the
$I=3/2$ channel.
