In this research, a novel numerical algorithm is introduced for computation of temperature-induced before crack steady strainstress field in plane-stress problem. For this purpose, two dimensional heat transfer equation and force equilibrium equations are sequentially solved using Galerkin Finite Volume method on identical unstructured triangular meshes when proper convergence for each field is achieved. In this model, a proper thermal boundary condition that is suitable for unstructured triangular meshes is introduced for analysis. Two test cases are used to assess accuracy of thermal and structural modules of the developed solver and the computed results are compared with theirs analytical solution.First, thermal analysis is performed for a rectangular plate which is connected to a supporting body with constant temperature and expose to surrounding liquid at three edges.Second, structural analysis is performed for a plate under distributed loads in two directions. Having obtained acceptable results from thermal and structural modules, thermal stress analysis is performed for a plate with fixed-end condition at one of edges,due to a uniform temperature field and the computational principle stress contours are compared with the Finite Element method results which have been reported in the literatures.