We have studied the properties of various isobars with 54 less than or
equal to A less than or equal to 64 for temperatures T less than or e
qual to 1.2 MeV via Monte Carlo shell model calculations with the KB3
interaction. In accord with empirical indications, we find no systemat
ic temperature dependence of the symmetry energy coefficient, b(sym),
for T less than or equal to 1 MeV. This contradicts a recent suggestio
n that b(sym) increases by 2.5 MeV at this temperature, which would si
gnificantly alter the supernova explosion scenario.