Lightweight, superelastic foams that resist creep and fatigue over a broad temperature range are being developed as structural and functional materials for use in numerous diverse applications. Unfortunately, conventional foams display superelasticity degradation, undergo considerable creep, show fatigue under repeated usage, or fracture over large strains, particularly under significant temperature variations. We have developed lightweight (density ≈ 14 mg/mL; corresponding volume fraction ≈ 9 × 10^-3) graphene-coated single-walled carbon nanotube (SWCNT) aerogels that remain superelastic, and resist fatigue and creep over a broad temperature range of -100–500 °C. We fabricate these materials by first creating a three-dimensional inelastic network of SWCNTs and then coating the junctions between SWCNTs with 2–5 layers of ≈ 3 nm long graphene nanoplatelets. Compressive stress (σ) versus compressive strain (ε) curves show that the aerogels fully recover their shapes even when strained by at least 80% over -100–300 °C and 20% at 500 °C, while the Young’s modulus remains similar over the temperature (-100–500 °C) and strain rate (0.01–0.16 1/s) ranges. The storage (E′) and loss moduli (E″) measured in the linear regime show ultralow damping ratio (tan δ = E″/E′) ≈ 0.02, and these viscoelastic properties remain constant over three decades of frequencies (0.628–628 rad/s) and across -100–500 °C. The low loss in these aerogels is corroborated by exceptional fatigue resistance for 2000 (5 × 10⁵) cycles at ε = 60% (1%) from -100–300 °C (-100–500 °C) and creep resistance at least under σ = 20 kPa, corresponding to ε = 4%, for a minimum of 30 minutes from -100–300 °C. Interestingly, the aerogels can be readily densified while retaining the microstructure and temperature-invariant thermomechanical properties to at least a volume fraction of 0.26 that reach E′ ≈ 1 GPa. The mechanical properties, high surface area, and large porosity make these aerogels highly suitable electrodes for electrochemical applications. For example, these aerogels show a high capacitance in both aqueous and room-temperature ionic liquid (RTIL) electrolytes, achieving between 60 and100 F/g, respectively, with the performance stable over hundreds of charge/discharge cycles and at high rates exceeding 1 V/s. This performance is retained fully under 90% compression of the systems, allowing us to construct cells with high volumetric capacitances of ≈ 5−18 F/cm³ in aqueous and RTIL electrolytes, respectively. Furthermore, the aerogels can be coated with noble metals and metal oxides to fabricate electrodes for fuel cells and pseudocapacitors, respectively, without compromising the mechanical properties. The emergent thermomechanical stability of these aerogels that arises from, in part, microscopic deformations of the graphene-coated junctions, motivate junction modification as a means to generate emergent properties in CNT. For example, substituting graphene with other two-dimensional materials such as boron nitride that also impart superelasticity to SWCNT aerogels, could add other desirable properties such as chemical inertness to temperature invariance. This work has been partially supported by the NSF through Grant CMMI 1335417 and US Army Research Office through grant W911NF-14-1-0651.