To analyze the thermal stress problem of thin conical shells, the basic thermoelastic differential equations of thin conical shells are established; the displacement and thermal stress in conical shells under temperature field are analyzed, using the distributed transfer function method. The calculation results show that the solution obtained by the distributed transfer function method matches well with the solution of the finite element method. The proposed method is able to analyze the thermal stress in thin conical shells with arbitrary boundary conditions and other loads; besides it can be further extended to the case of revolution shells with curvilinear generatrix.