A detailed analysis of the cooling and thermalization process for photogenerated carriers in semiconductor quantum wires is presented. The energy relaxation of the nonequilibrium carrier distribution is investigated for the ``realistic'' case of a rectangular multisubband quantum-wire structure. By means of a direct ensemble Monte Carlo simulation of both the carrier and the phonon dynamics, all the nonlinear phenomena relevant for the relaxation process, such as carrier-carrier interaction, hot-phonon effects, and degeneracy, are investigated. The results of these simulated experiments show a significant reduction of the carrier-relaxation process compared to the bulk case, which is mainly due to the reduced efficiency of carrier-carrier scattering; on the contrary, the role of hot-phonon effects and degeneracy seems to be not so different from that played in bulk semiconductors.