Li-ion batteries suffer from two key safety issues: thermal overload and compression recovery, which may lead to flammability and mechanical failure. Silica aerogels are promising solutions to both these issues owing to their excellent thermal stability and tailored mechanical properties. However, finding the optimum sol composition in sol-gel-based aerogel synthesis is needed to address these issues at industry-relevant scales. Here, we propose an innovative approach to determine the optimum sol composition for methylsilsesquioxane (MSQ) aerogel sheets, which is based on the mechanisms of the effects of molar ratios of hydrolysis water and isopropyl alcohol (IPA) to methyltrimethoxysilane (MTMS) on the physical properties of MSQ aerogel sheets and according to the ternary contour distribution of their properties. The synthesized MSQ aerogels exhibited a soft, light, and powderless texture and featured superhydrophobic properties (150.2°), low thermal conductivity of 33.6 mW/(m·K), high thermal stability temperature in nitrogen atmosphere at 479.3 °C and moderate short-term (<6 h) service temperature of 120.0 °C. Significantly, the structural stability and elasticity of the aerogels surpassed the current state-of-the-art, showing recovery to 81.3 % of the original thickness and 85.2 % of the original stress after being subjected to 400 cycles of high-speed and high-strain consecutive compression, respectively. These excellent properties make the MSQ aerogel sheets promising for applications in thermal load and compression recovery management of diverse energy storage devices, including batteries for next-generation electric vehicles