  In a chiral $U_L(N)\times U_R(N)$ fermion model of NJL-form, we prove that,
if all the fermions are assumed to have equal masses and equal chemical
potentials, then at the finite temperature $T$ below the symmetry restoration
temperature $T_c$, there will be $N^2$ massive scalar composite particles and
$N^2$ massless pseudoscalar composite particles (Nambu-Goldstone bosons). This
shows that the Goldstone Theorem at finite temperature for spontaneous symmetry
breaking $U_L(N)\times U_R(N) \to U_{L+R}(N)$ is consistent with the real-time
formalism of thermal field theory in this model.
