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In order to meet stringent temperature-control requirements in a high-speed airflow wind tunnel (HAWT) for thermal simulation under complicated work conditions such as thermal strength experiment of aero engine blade and dynamic calibration of high temperature thermal coupler, this paper proposes a novel cascade fuzzy-PID (C-Fuzzy-PID) compound control method for regulating the fuel-oil flow rate in the inner loop and temperature in the outer loop. The mathematical models that characterize the dynamics of the heat airflow temperature in the combustor and the fuel-oil flow rate for combustion are derived, upon which the improved PID control laws for the inner and outer loops are described. The former employs a fuzzy-PID controller with a predictor for controlling flow rate in the inner loop, which effectively overcomes influences according to its characteristics of large inertia and transport lag in fuel-oil supply system on the temperature responses. The latter combines disturbance compensation and a fuzzy-PID feedback law to suppress influences due to factors such as change in work conditions, disturbances, and time-varying parameter variations. The C-Fuzzy-PID method has been numerically investigated by comparing simulation results against two traditional PID-based methods, as well as experimentally validated confirming that the proposed control algorithm has strong robustness and excellent adaptability for temperature control of an HAWT.