  The temperature dependence of the nuclear matter isovector symmetry energy
coefficient ($\cA_{0,1}$) is investigated in the framework of the generalized
nuclear polarizability with Skyrme interactions, as worked out in Refs.
\cite{npa,prc}. The variation of $\cA_{0,1}(T)$ is very small (of the order of
1 MeV) for temperatures (T) in the range of 0 and 18 MeV. Different behaviors
with temperature are found strongly depending on the Skyrme parameterization,
in particular at densities lower than the saturation density $\rho_0$.
