We perform binary neutron star merger simulations using a newly derived set of finite-temperature equations of state in the Brueckner-Hartree-Fock approach. We point out the important and opposite roles of finite temperature and rotation for stellar stability and systematically investigate the gravitational-wave properties, matter distribution, and ejecta properties in the postmerger phase for the different cases. The validity of several universal relations is also examined and the most suitable EOSs are identified.