We have experimentally studied the pump-probe Kerr rotation dynamics in WSe2 monolayers. This yields a direct measurement of the exciton valley depolarization time τv. At T=4K, we find τv≈6 ps, a fast relaxation time resulting from the strong electron-hole Coulomb exchange interaction in bright excitons. The exciton valley depolarization time decreases significantly when the lattice temperature increases, with τv being as short as 1.5 ps at 125 K. The temperature dependence is well explained by the developed theory, taking into account the exchange interaction and fast exciton scattering time on the short-range potential.