For a Grashof number that is large compared to unity, we expect that the resistance to heat transfer, alternatively the region where most of the temperature change occurs, will be confined to a thin region close to the surface.  If this region is thin compared to the macroscopic dimensions, we expect that boundary-layer approximations will give valid simplifications to the governing equations.  This will be the case.  Thus the boundary-layer equations will serve as the basic theory for the convection/conduction heat transfer from the heated sphere.