With the growing demand for insulation parts in extreme service environments, such as nuclear power, aviation, and other related fields, fiberglass-reinforced silicone resin (FRSR) has become a popular choice due to its exceptional physical and chemical properties in high-temperature and electromagnetic working environments. To enhance the performance of FRSR molded parts that can adapt to more demanding extreme environments, the oven postcuring process parameters on thermal stability and mechanical properties of the bobbin were investigated. The curing behavior of FRSR was analyzed by using thermogravimetric analysis (TGA) and the differential scanning calorimetry (DSC) method, and the bobbins were manufactured based on the testing results. Subsequently, the bobbins were oven postcured at different conditions, and the heat resistance and mechanical properties were analyzed by TGA and tensile tests. The results revealed that the tensile strength of the bobbin increased by 122%, and the weight loss decreased by 0.79% at 350 °C after baking at 175 °C for 24 h. The optimal process parameters for producing bobbins to meet the criteria of nuclear installations were determined to be a molding temperature of 120 °C, molding pressure of 50 MPa, pressure holding time of 3 min, oven postcuring temperature of 175 °C, and postcuring time of 24 h. The molded products have passed the thermal aging performance test of nuclear power units.