We investigate the use of hybrid equations of state in binary neutron-star simulations in full general relativity, where thermal effects are included in an approximate way through the adiabatic index Γth. We employ a newly developed finite-temperature equation of state derived in the Brueckner-Hartree-Fock approach and carry out comparisons with the corresponding hybrid versions of the same equation of state, investigating how different choices of Γth affect the gravitational-wave signal and the hydrodynamical properties of the remnant. We also perform comparisons with the widely used Steiner-Fischer-Hempel equation of state, detailing the differences between the two cases. Overall, we determine that when using a hybrid equation of state in binary neutron-star simulations, the value of the thermal adiabatic index Γth ≈ 1.7 best approximates the dynamical and thermodynamical behavior of matter computed using complete, finite-temperature equations of state.