  We compute the free energy of asymmetric nuclear matter in a
Brueckner-Hartree-Fock approach at finite temperature, paying particular
attention to the dependence on isospin asymmetry. The first- and second-order
symmetry energies are determined as functions of density and temperature and
useful parametrizations are provided. We find small deviations from the
quadratic isospin dependence and very small corresponding effects on
(proto)neutron star structure.
