The development of temperature-insensitive stretchable conductors has significant implications for a wide range of applications, including wearable electronics, flexible sensors, and stretchable circuits in different environments, while resistances of conductive polymer composites are generally temperature dependent. In this study, we develop a novel and facile approach to achieve stable electrical conducting under stretching and temperature variation by incorporating a hierarchical wavy graphene foam (wGF) with a double-layer conductive framework formed by coating highly conductive poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) on interior graphene struts. The resulting wGF/PEDOT:PSS/PDMS composites exhibit exceptional resistance stabilities during stretching within a wide temperature range of -30-145 °C. The synergistic effects of the unique composite structure, including the macroscopic wavy structures, microscopic compacted conductive skeletons, and more ductile double-layer graphene/PEDOT:PSS frameworks, contribute to the excellent stretchable conducting properties and temperature-insensitive performances. The developed temperature-insensitive stretchable conductor holds great promise for reliable performance in various environmental conditions, opening up new opportunities for advanced flexible and wearable electronic devices.