In the present work, the equation of state of hot asymmetric nuclear matter nas Been investigated in the framework of the finite temperature Brueckner-Hartree-Fock (FTBHF) approach with a microscopic three-body force (TBF). The temperature dependence and the isospin dependence of the single particle properties, such as the proton and neutron single-particle potentials and effective masses have been studied. It is shown that the TBF gives a repulsive contribution to the proton or neutron single particle potential. The energy per nucleon versus asymmetry parameter is found to fulfill a parabolic relation as in the zero temperature case[I]. This means that the symmetry energy at finite temperature Esym can be extracted from' the energy difference between pure neutron matter and symmetric matter. The calculated symmetry energy is plotted in Fig.1. It