Numerical simulations for the merger of binary neutron stars are performed in full general relativity incorporating a finite-temperature ( Shen ’ s ) equation of state ( EOS ) and neutrino cooling for the first time . It is found that for this stiff EOS , a hypermassive neutron star ( HMNS ) with a long lifetime ( \gg 10 ms ) is the outcome for the total mass \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } 3.0 M _ { \odot } . It is shown that the typical total neutrino luminosity of the HMNS is \sim 3 – 8 \times 10 ^ { 53 } erg/s and the effective amplitude of gravitational waves from the HMNS is 4– 6 \times 10 ^ { -22 } at f = 2.1 –2.5 kHz for a source distance of 100 Mpc . We also present the neutrino luminosity curve when a black hole is formed for the first time .