Infrared thermal imaging technology is widely used in the study of precursor characteristics and early warning methods of rock failure. However, infrared radiation precursory features have many forms, so it has certain influence on the accurate early warning of rock instability. The failure and instability of rock are closely related to the evolution of strain energy, and the infrared radiation information of rock is related to the dissipation and release of strain energy. If the strain energy is combined with infrared radiation information, the rock failure and instability can be monitored and warned accurately. Based on this, in this paper, the release time of elastic energy is determined by the cusp mutation theory based on the energy evolution characteristics, which is combined with the infrared radiation anomaly information to determine the precursor of rock failure and instability. The results show that with the sudden drop of the elastic energy curve, the infrared radiation synchronization appears abrupt change. The elastic energy release time of sandstone predicted by constructing the sharp point mutation model can be divided into two situations: leading and lagging the first mutation time of infrared radiation. Taking the elastic energy release time as the standard, the infrared radiation mutation near the sandstone can be regarded as the precursor of sandstone failure. The results can provide a new idea for mine disaster monitoring and early warning.