Electricity demand has surged over the last several years and will persist in the future. Increased transmission loads cause transmission lines to operate much closer to their security limits, leading to thermal and mechanical stress and thus affecting the transmission reliability and thermal aging. Accordingly, monitoring the conductor temperature over time is critical to identifying power transmission networks that may need extra attention and perhaps maintenance. This paper presents a fuzzy thermal aging model for transmission lines equipped with a fuzzy dynamic thermal rating system based on the IEEE 738 standard. In this framework, the ampacity of the transmission line was calculated. The conductor temperature was computed with the back-calculation method by considering the fully loaded transmission line. The estimated conductor temperature was employed to determine the corresponding conductor fuzzy loss of tensile strength, i.e., the fuzzy annealing degree of the conductor based on the Harvey model. Additionally, a tensile strength loss cost profile is provided. Simulation and numerical results indicate that the proposed framework is robust against various operating conditions of the parameters considered in the study and provides crucial information for managing transmission assets and transmission network operation.