The effect of elevated curing temperature on the fracture properties of concrete was investigated. Fracture experiments were carried out on wedge splitting specimens exposed to temperatures ranging from 5 to 60 °C. A new maturity model was then proposed for describing the combined influence of the temperature and aging on the fracture properties of concrete. The results show that the fracture energy of concrete subjected to high temperature is high at early ages; however, the effect of curing temperature on the fracture energy was reversed after 14 days, with greater later-age fracture energy corresponding to lower temperature and vice-versa. The effective fracture toughness of concrete also exhibited the same temperature inversion phenomenon. The optimum curing temperature was found to be approximately 40 °C for development of concrete fracture properties. The value of activation energy changed with fracture properties, temperature ranges and the development stage of a given fracture property. The proposed model accurately predicts the fracture properties of concrete and significantly simplifies the calculation process of the maturity index relative to the existing maturity method.