In this paper, 650 V / 7.5 A rated enhancement-mode (E-mode) Gallium Nitride (GaN) highelectron-mobility-transistors (HEMTs) with integrated gate drivers are characterized under thousands of accelerated thermal cycles (ATC) at different junction temperature stresses. This research helps in developing fundamental insights into GaN HEMTs' aging characteristics through the degradation of ten devices under ATC tests. For over 20,000 thermal cycles, the forward and reverse conduction losses, IGSS, Coss, and the RDSon are experimentally measured to identify the parameter shifts and the corresponding precursors. Results indicate that both IGSS and Coss do not deviate much, but the values of RDSon, the forward and reverse conduction losses vary considerably with device aging. This paper also presents an empirical method to estimate the correlation between the acceleration factors of the GaN FETs' degradation process and the thermal cycling conditions. The value of the activation energy of the tested GaN HEMT devices is also derived using the empirical equations to be about 1.13 eV under the applied stress factors. This study finds that the degradation process of GaN HEMTs with age facilitates a reasonable correlation with different failure mechanisms, which further helps in reliability improvement.