Abstarct: In this study, an exact analytical solution for steady and unsteady heterogeneous conductive heat transfer in spherical laminated composite vessels is presented. This study focuses on axisymmetric heat transfer in spherical composite laminates by considering the heat conduction in Peripheral and radial dimensions. This analytical solution is also obtained for general linear thermal boundary conditions which covers combined effect of the heat conduction, convection, and radiation at boundaries. Finding the most generalized analytical solution baxsed on the complicated boundary conditions and heterogeneous heat transfer is one of the main innovation of current work. for solving the steady-state problem. first, Kirchhoff transformation is used to homogenize the temperature equation and then the problem solved in the Kirchhoff environment by using the separation variable method. Finally, by Kirchhoff inverse transformation the temperature equation was obtained in the desired physical environment. in order to solve the problem unsteady state the equation was converted by the superposition method to steady and unsteady parts. and then by using Kirchhoff transformation and the separation variable method the temperature equation of the unsteady part was obtained. then the final temperature equation be came the sum of the unsteady and steady parts. Finally, MATLAB software was used for analytical solve the temperature equation for different boundary conditions and for validation of this work, the temperature values and diagrams obtained were compared with the values obtained from the numerical solution. Finally, conclusions were done from the present study and some suggestions.