The equation of state of asymmetric nuclear matter at finite temperature is studied in the framework of the Brueckner-Hartree-Fock approximation which is extended to include three-body force correlations. Due to the additional repulsion produced by three-body force contribution, the proton or neutron potential energy and effective mass are correspondingly enhanced. The symmetry energy gradually becomes more sensitive to the temperature with the increasing density compared with the result that only includes the two hole-line contribution.The asymmetry parameter dependence of symmetry energy is also indicated. It is shown that there is the same linear relation between symmetry energy and β2 as the zero temperature case with β being the asymmetry parameter.