Solid heat spreaders, particularly those made of copper or graphite, are often benchmark solutions for hotspot thermal management. In this paper, we present exact and approximate analytical solutions of steady-state hotspot cooling with a planar heat spreader, which is subjected to adiabatic conditions except for a hotspot centered at the top surface and a constant temperature at the bottom surface. The approximate solution bridges exact solutions at two limits of hotspot size: infinitesimal hotspot at the center and uniform heat flux across the spreader. The approximate solution accounts for variable hotspot size and anisotropic thermal conductivity in a compact form, which is useful for estimating thermal parameters such as conduction shape factor and effective thermal conductivity.