The properties of hot asymmetric nuclear matter are studied in the framework of the finite temperature BruecknerHartree-Fock theory that is extended to include the contribution of microscopic three-body forces. We give the variation of the critical temperature with the asymmetry parameter and show the effect brought by this three-body repulsive potential on the value of the critical asymmetry of the phase transition for asymmetric nuclear matter. Owing to the additional repulsion provided by three-body forces, this value decreases. In addition, the domain of mechanical instability for hot nuclear matter is also indicated, which gradually shrinks with increasing asymmetry and temperature.