A spatial inverse distance interpolation algorithm based on KD-tree and a radial basis function interpolation algorithm based on pseudo-inverse matrix, are proposed to address the problem of temperature interpolation between unmatched meshes in the finite element model for heat transfer analysis and the finite element model for stress analysis. Firstly, to deal with the low efficiency of nearest neighbor node search caused by the large scale of the finite element model, a spatial KD-tree structure of all known nodes is constructed, and a neighborhood node search algorithm based on KD-tree is designed. Then, based on the coordinates and temperatures of the known nodes in the neighborhood, the inverse distance weighting interpolation for the unknown nodes is implemented. Secondly, regarding the singularity problem of the linear equation system matrix used to calculate the coefficients of the interpolation function, radial basis interpolation functions are constructed with the basis function \(r^{3}\) . Based on the coordinates and temperatures of known nodes, a linear equation system for calculating the coefficients of the interpolation function is established. The approximate values of the coefficients of the interpolation function are calculated using the pseudo-inverse matrix method, realizing the radial basis function interpolation for the unknown nodes. Three types of finite element models were constructed and compared using the two interpolation algorithms. The inverse distance weighting interpolation algorithm showed poor interpolation accuracy at positions with high temperature gradients, with average errors of 3.37, 1.53, and 3.90% for the three types of structures, respectively. The radial basis function interpolation algorithm showed higher accuracy, with average errors of 0.17, 0.28, and 1.84% for the three types of structures, respectively.