Temperature dependence of the nuclear symmetry energy

We have studied the properties of A=54 and A=64 isobars at temperatures T \leq 2 MeV via Monte Carlo shell model calculations with two different residual interactions. In accord with empirical indications, we find that the symmetry energy coefficient, b_{sym}, is independent of temperature to within 0.6 MeV for T \leq 1 MeV. This is in contrast to a recent suggestion of a 2.5 MeV increase of b_{sym} for this temperature, which would have significantly altered the supernova explosion scenario.