Thermalization of near-band-gap excited carriers in an intrinsic GaAs quantum well is studied using ensemble Monte Carlo simulation. Carrier-carrier interaction is treated like two-particle collisions due to the screened Coulomb interaction. The indistinguishability of two colliding electrons (holes) is included by taking into account the exchange electron-electron (hole-hole) scattering between the electrons (holes) of like spin. The model is modified to the case of spin-polarized carriers. We show that the thermalization of the spin-polarized carriers is several times slower than the thermalization of the spin-randomized ones when the carrier density exceeds 10(11) cm-2. The effect is due to the exchange scattering, which significantly weakens the direct Coulomb scattering in the dense carrier gas. For small densities the exchange becomes negligible. Possibilities to observe the exchange experimentally are discussed.