The semiconductor industry is experiencing significant growth in production scale and investment, driven by rising demand for generative AI, high-performance computing (HPC), high-bandwidth memory (HBM), and high-performance/high-density chips. As a result, precision inspection and yield management at the wafer stage have become critical challenges. Probe cards, essential for verifying a chip's electrical performance, play a vital role in yield management. However, during repetitive inspection processes, probe cards absorb heat from the underlying chuck, leading to probe tip-pad alignment errors that degrade contact reliability and measurement accuracy. This situation necessitates a quantitative evaluation system based on thermo-structural coupled analysis. Additionally, the modeling process for multiple interposers and interposer housings, along with the preprocessing of contact conditions, adds complexity due to the increasing number of contact surfaces. This complexity can result in convergence issues and reduced accuracy. To address these challenges, this study employs Ansys Parametric Design Language (APDL) to enhance interposer and housing modeling, as well as contact problem resolution. It introduces a novel meshing method that positions nodes at target coordinates using point clouds, providing an effective analysis approach applicable to large, high-density probe cards and thermo-structural problems involving numerous contacts.