Use of recycled aggregates (RA), obtained from construction and demolition waste, to prepare concrete is very much relevant to ensure sustainable development. Although significant amount of data is available for mechanical properties of recycled aggregate concrete (RAC) at ambient temperatures, data regarding the residual stress–strain relationship of RAC after exposure to elevated temperatures is very limited. Focus of this paper is, therefore, to experimentally investigate residual mechanical properties along with residual stress–strain relationship of concrete mixes prepared with recycled aggregates (RA) subjected to elevated temperatures. Concrete cylindrical specimens cast with 30% RA were used in the experimental program. The specimens were first exposed to various elevated temperatures ranging between 100 and 1000 °C at an interval of 100 °C, and were then tested under compression and tension after being brought to ambient temperature. Various properties including residual compressive and splitting tensile strengths, Poisson’s ratio, and modulus of elasticity along with stress–strain behavior were investigated in this study. Change in color of concrete was noticed after 300 °C; while, surface cracks were observed at 500 °C. After 600 °C, substantial loss in concrete compressive and tensile strengths, and stiffness was observed.