Abstract: Thermal stability of liquid jet is the deeper discussion to jet stability, which can improve our understanding to the mechanism of breakup and atomization of liquid jet. Also, Study on the thermal stability of liquid jet has an important value in theory and engineering. Based on the jet stability theory, under the conditions of gas rotation, fluids compressibility and supercavitation, this paper gives the mathematical model describing the thermal stability of supercavitating jet in a compressible rotary gas, and the corresponding numerical method for solving the mathematical model is proposed and verified by the data in reference. Then, this paper analyzes the effects of gas-liquid temperature differences and temperature gradients on jet instability, and studies the thermal stability of supercavitating jet. The results show that the maximum disturbance growth rate, the dominant frequency and the maximum disturbance wave numbers increase linearly with the increasing of gas-liquid temperature differences. The existence of temperature gradient inside the jet makes the instability effects of temperature differences on jet more obvious. The temperature gradients will inhibit the effects of supercavitation on jet instability, while gas-liquid temperature differences will promote the effects of supercavitation on jet instability.