We examined the thermal characteristics of the E' (E′1) center in gamma-ray irradiated natural quartz using electron spin resonance (ESR) spectroscopy. Assuming first order kinetics, we suggested a mechanism and, consequently, an analytical model to explain the thermal evolution of the effective concentration of E′ point defect. The model was used to track the ESR evolution of E′ centers signal while taking into account the existence of two independent types of E′ centers. The kinetic characteristics (activation energy and frequency factor) of both E′ centers were found to be slightly different. The activation energies of thermal production and annihilation of these two centers were shown to be different from process to another and to be linearly dependent on their associated frequency factors in respect to the accumulated gamma-dose, following the Meyer-Neldel rule. As a result, one of the two E′ is shown to have been irradiation-annihilated like center, while the other is found to have been irradiation-induced like center.