Abstarct: In present study, an analytical solution is presented for the problem of anisotropic heat conduction in heterogeneous composite conical shells. The shell is consider to have a full conical shape and fibers are winded in an arbitrary angle leading to anisotropic nature of heat conduction in the conical shell. Therefore, the fiber angle could be considered from zero to 90 degrees. In order to obtain the most general solution, the general boundary condition is considered at the basis of shell. Heat convection between conical shell and ambient flow, and an external source of radiative heat transfer were also modeled in the heat transfer partial differential equation. Herein, the heterogeneity of heat transfer is the direct result of dependence of the conductivity coefficient on temperature. For solving the steady state heterogeneous heat conduction problem, the Kirchhoff transformation followed by an integral transform method are applied. The Green’s functions are used to solve the final ordinary differential equations. In other to solve the heterogeneous heat conduction problem in unsteady state, the Kirchhoff transformation followed by an integral transform method are applied. By means of an integral transform in angular direction, the heat conduction equation is transformed and after that the transferred heat equation is solved using separation of variables method. Eventually, an inverse transformations is used in order to achieve the final exact solution of heterogeneous anisotropic conductive heat transfer equation. To verify the accuracy of present analytical solution, second order finite difference solution was obtained. The analytical results show a good agreement with numerical data. The applicability of our analytical method is tested with solving real industrial examples. Herein, the temperature distributions in a typical pressure vessel and a pin fin are calculated analytically.