We perform a systematic calculation of the equation of state of asymmetric nuclear matter at finite temperature within the framework of the Brueckner-Hartree-Fock approach with a microscopic three-body force.When applying it to the study of hot kaon condensed matter, we find that the thermal effect is more profound in comparison with normal matter, in particular around the threshold density.Also, the increase of temperature makes the equation of state slightly stiffer through suppression of kaon condensation.