We consider the thermal boundary layer beneath the surface of a differentially heated fluid portion of a rotating sphere, i.e., a region in which thermal conductivity is important but viscosity is negligible. A general three-dimensional similarity transformation is performed, and features of the related temperature and flow fields are studied. It is found that an upwelling of cold water into the boundary layer region from below is always necessary, that horizontal advection of heat is relatively negligible, and that a strong relation exists between boundary layer depth and surface-forcing function. The solutions are examined for numbers characteristic of the main oceanic thermocline.