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In view of the time-varying complexity of the heat source for the ball screw feed system, this paper proposes an adaptive inverse problem-solving method to estimate the time-varying heat source and temperature field of the feed system under working conditions. The feed system includes multiple heat sources, and the rapid change of the moving heat source increases the difficulty of its identification. This paper attempts to develop a numerical calculation method for identifying the heat source by combining the experiment with the optimization algorithm. Firstly, based on the theory of heat transfer, a new dynamic thermal network model was proposed. The temperature data signal and the position signal of the moving nut captured by the sensors are used as input to optimize the solution of the time-varying heat source. Then, based on the data obtained from the experiment, finite element software parametric programming was used to optimize the estimate of the heat source, and the results of the two heat source prediction methods are compared and verified. The other measured temperature points obtained by the experiment were used to compare and verify the inverse method of this numerical calculation, which illustrates the reliability and advantages of the dynamic thermal network combined with the genetic algorithm for the inverse method. The method based on the on-line monitoring of temperature sensors proposed in this paper has a strong application value for heat source and temperature field estimation of complex mechanical structures.