Traditional finite element models are usually established based on specific structures to address the transient nonlinear heat transfer analysis; however, if the structure parameters change one has to reanalyze/rebuild the finite element models, resulting in a lot of additional computational cost. To address this problem, this work develops a generic grid refinement approach to improve the computational efficiency of nonlinear heat transfer analysis. The advantage of the proposed method lies that the grids can be used to establish connections between original and modified structures through transfer operators, which is calculated only once for the original structures and can be reused in following grid iterations. Then, the transient nonlinear heat transfer equations of modified structures can be efficiently solved based on the grid iterations in each time step. As a result, the computational cost can be magnificently reduced. Several numerical examples are investigated to comprehensively evaluate the performance of the present algorithm when dealing with the transient nonlinear heat transfer analysis of structures with modifications.