Gallium nitride high-electron-mobility transistors (GaN HEMTs) are critical for high-power applications like AI power supplies and robotics but face reliability challenges due to increased dynamic ON-resistance (R_{DS_ON}) from electrical and thermomechanical stresses. This paper presents a novel self-calibrating temperature-sensitive electrical parameter (TSEP) model that uses gate leakage current (I_G) to estimate junction temperature with high accuracy, uniquely addressing aging effects overlooked in prior studies. By integrating I_G, aging-induced degradation, and failure-in-time (FIT) models, the approach achieves a junction temperature estimation error of less than 1%. Long-term hard-switching tests confirm its effectiveness, with calibrated R_{DS_ON} measurements enabling precise remaining useful life (RUL) predictions. This methodology significantly improves GaN HEMT reliability assessment, enhancing their performance in resilient power electronics systems.