  The gap equation at finite temperature in the top-quark condensate scheme of
electroweak symmetry breaking is proved to have the identical form in both the
imaginary and the real time formalism of thermal field theory. By means of the
gap equation, combined with the basic relation to define the vacuum expectation
value $v$ of the effective Higgs field, we analyse the dependence on
temperature T and chemical potential $\mu$ of the dynamical top-quark mass as
the order parameter characteristic of symmetry breaking, and obtain the $\mu-T$
criticality curve for symmetry restoration. We find out that the critical
temperature $T_{c}=2v$ for $\mu=0$ and the critical chemical potential
$\mu_c=2\pi v/\sqrt{3}$ for T=0. When $\mu=0$, the top-quark mass near $T_c$
has the leading ${(T_c^2-T^2)}^{1/2}$ behavior with an extra factor dependent
on temperature $T$ and the momentum cut-off $\Lambda$. However, it is generally
argued that the symmetry restoration at $T\geq T_c$ is still a second-order
phase transition.
