In gas turbine, the interaction between hot gas mainstream and blade solid region becomes more and more obvious as the turbine inlet temperature increases, thus heat conduction within the blade solid regions should be taken into consideration in optimization design process. In this paper, an adjoint-based optimization method for heat conduction problems in the solid region was built based on ANSYS Fluent and OpenFOAM Solver. The continuous adjoint equation and the corresponding boundary conditions for three typical conduction boundary conditions were derived in detail. To validate the correctness of this method, inverse design problems within the hollow cylinder and hollow blade were calculated, respectively. Inner shape inverse design of the hollow cylinder and the blade thickness inverse design were performed, and the target values were found successfully. Adjoint gradients were compared with finite-difference method or theoretical results. Then a Conjugate Heat Transfer (CHT) calculation was performed using ANSYS Fluent software, and the numerical methods were validated against the experimental results. An optimization of the struts place and thickness within hollow blade for average temperature was performed based on the CHT calculation results. Average temperature within the solid region of the optimized blade decreased 11.1K as compared to the original case.