Abstarct: One of the most important issues in the design of engineering structures is preventing the structure from breaking due to the stress created in the areas of geometric discontinuity. The presence of an opening in the functional variable plate under heat flow causes thermal stresses around the opening. The type of geometry of the opening is one of the important parameters in how the stress is distributed around it. In this thesis, by extending the Goodyear-Florence method, thermal stress analysis of a functionally variable plate with a non-circular opening has been studied. Using the mixed variable method, they obtained the stress distribution around circular and oval openings in isotropic plates. By expanding this method for the functional variable plane and using the harmonic mapping function, the stress distribution around the non-circular opening is investigated. For this purpose, exponential function has been used for the examined page. In this research, the effect of various parameters on the stress distribution around the opening, such as the rotation angle of the opening, the heat flux angle, the geometry of the opening, and the curvature of the corners of the opening, is investigated. According to the obtained results, it can be seen that, contrary to expectations, the circular opening is not always the best geometry to reduce the stress concentration, and in some cases, by choosing the appropriate geometry and rotation angle for the opening, it is possible to have less stress concentration compared to the circular opening. The main goal of this thesis is to investigate and analyze the thermal stress of a functional variable plate that has an opening in the center. The dimensions of the screen compared to the dimensions of the opening are considered so that it can be assumed to be infinite. The loading of the plate in the form of heat flux is uniform. The plate has linear elastic behavior.