Transient aerodynamic heating experiments with high-speed aircraft require temperature sensors that can carry out rapid and accurate electromotive force (EMF)–temperature conversions. A fast, high-precision non-linear EMF–temperature conversion method is proposed. In this method, the temperature values to be converted were pre-positioned using a non-linear mathematical model. Then, they were accurately positioned using an efficient binary search algorithm with a small scope. Thus, this method has rapid conversion speed and high calibration precision. This conversion precision is enhanced by one order of magnitude over that of the normal reference table, and the conversion time is 1% of that of the traditional piecewise linearization method. This method was employed in a transient aerodynamic heating experimental simulation system with high-speed aircraft. The experiment results show that, in the case of a high change rate of temperature and heat flux, accurate dynamic tracking can still be realized, and the experimental simulation results agree well with the pre-set environment. The developed temperature sensor calibration method is necessary for high-speed and high-precision aerodynamic heating experiments with hypersonic aircraft.