In part I the steady and unsteady local temperature distribution has been obtained for mixed prescribed boundary conditions on the spherical surface. The case of prescribed heat flux in a given  - range and prescribed temperature distribution on the remaining  - range has been determined for the axi-symmetric case. This was also obtained for the unsteady case with a given initial condition. For an annular spherical system the inner spherical surface was considered at given constant tempe­rature. In part II the steady and unsteady temperature distribution has been determined for a conical body exhibiting on the conical surface constant tempe­rature and on the spherical surface mixed boundary conditions. Part of the spherical surface exhibits a prescribed heat flux while the remaining part shows a prescribed temperature distribution. The axi-symmetric temperature distribution has been determined for various ranges of these boundary conditions. The unsteady temperature distribution has also been obtained for a given initial condition.