Accurately and efficiently determining time-varying thermal loads, such as heat flux, in solid structures is of great importance for transient nonlinear heat conduction engineering problems. Usually, measuring temperatures at accessible locations and solving the ill-posed inverse problem are the solutions to identify unknowns. By minimizing the discrepancy of measured and simulated temperatures, the optimal values related to thermal loads can be obtained. However, repeated calculations during optimizations lead to low computational efficiency. In order to improve the computing speed of direct problems using traditional numerical computational methods, an alternating iteration strategy combining finite element method with reduced-order modeling (FEM-ROM) is proposed in this paper, in which the proper orthogonal decomposition (POD) technique is used to establish a sectionalized extrapolation algorithm with lower dimensions and sufficiently high accuracy. This iteration strategy reduces the computational scales by using the ROM technique and guaranteeing the accuracy by continually correcting the databases and POD bases every few time steps during the process of iterations. In the inversion process, FEM-ROM is responsible for the part of forward calculations and the Levenberg-Marquardt algorithm is used as a gradient based method to update parameters in each time steps. Finally, the accuracy and efficiency of the proposed strategy is demonstrated by several examples.