We have utilized subpicosecond laser pulses to excite and probe hot electrons and nonequilibrium longitudinal-optical (LO) phonons in bulk GaAs by Raman scattering. We find that the photoexcited hot electrons cool at a rate much faster than predicted by intravalley scattering of LO phonons via the Frolich interaction. On the other hand, this fast cooling rate can be accounted for satisfactorily by intervalley scattering. As a result of this very rapid cooling, the temperature of the hot LO phonons generated by the hot electrons temporarily overshoots the electron temperature. From the electron cooling curve and the dependence of the hot-phonon temperature on the excited-electron density, we determined the deformation potential for scattering between the GAMMA and L conduction-band valleys in GaAs.