  We applied the Thermofield Dynamics formalism to analyze how the
non-classical properties of the Bell-Cat states are influenced by a gradual
change of temperature values, in a thermal equilibrium system. To this purpose
we calculate the thermal Wigner functions for these states, whose negative
volume is associated with non-classical properties, and we evaluate how these
non-classical features vary with temperature. Our results indicate that these
properties are almost absent for temperatures of around $2\mathrm{K}$.
