The equation of state (EOS) of ANM by using the Bruckner-Hartree-Fock (BHF) approach enhanced by integrating a phenomenological 3-body force (3BF), contact term (CT) and Dirac corrections are investigated in this paper. In the present BHF calculations we used two types of realistic nucleon-nucleon (N-N) interactions. One is the charge-dependent Bonn potential (CD-Bonn) and the other is local soft core Argonne (V18). We can be used the EOS to obtain the bulk properties of nuclear matter such as the pressure, the incompressibility and the symmetry energy. The good agreement is observed when compared between the previous theoretical estimates and experimental data. After that we study the thermal properties of asymmetric nuclear matter such as the pressure at T= 0, 4, 8, 12, 16, 20, 24, 28 and 32 MeV. Also, a critical temperature T_c for asymmetric nuclear matter is found and there is no phase transition at high asymmetry parameter (α).