We study spin dynamics of excitons confined in self-assembled CdSe quantum dots by means of optical orientation in magnetic field. At zero field the exciton emission from QDs populated via LO phonon-assisted absorption shows a circular polarization of 14%. The polarization degree of the excitonic emission increases dramatically when a magnetic field is applied. Using a simple model, we extract the exciton spin relaxation times of 100 ps and 2.2 ns in the absence and presence of magnetic field, respectively. With increasing temperature the polarization of the QD emission gradually decreases. Remarkably, the activation energy which describes this decay is independent of the external magnetic field, and, therefore, of the degeneracy of the exciton levels in QDs. This observation implies that the temperature-induced enhancement of the exciton spin relaxation is insensitive to the energy level degeneracy and can be attributed to the same excited state distribution.