In this work, thermally assisted OSL (TA-OSL) of natural fluorite was investigated, aiming to understand better the role of traps in both TL and OSL. TA-OSL is the luminescence simultaneously stimulated by light and heat; from this combination it is possible to access deeper traps in the analyzed material, that, in general, need more energy to be accessed. Irradiations were performed at room temperature using the Sr-90/Y-90 source incorporated in the TL/OSL reader at a dose rate of about 10 mGy/s. The optical stimulus was blue light at 470 nm. The dosimeters were also irradiated with X and gamma-rays of various energies (from 20 keV to 1.25 MeV) for comparing the energy dependence of the OSL and the TA-OSL signals. Residual TL curves were acquired after OSL readouts for checking trap participation in OSL emission. The OSL measurements were done at temperatures from 25 degrees C to 400 degrees C. For readout temperatures from 25 to similar to 185 degrees C, decay curves were observed, and they were modeled by one stretched-exponential function, giving rise to a good fit to the experimental data. The dependence of the fitting parameter (beta) on the photon energy was studied, and it was observed that beta increases with the X-ray beam effective energy. The energy dependence of OSL signal is 1.5 times larger than that of TA-OSL signal, pointing to the reduction in energy dependence with the combination of thermal and optical stimuli. The total light emitted (TA-OSL + residual TL) is highly increased by the simultaneous stimulation by light and heat, indicating that light promotes charges to thermally active traps (phototransfer), and heat promotes charges to optically active traps, facilitating their release during illumination.