Buoyancy driven thermal convection due to the presence of a sphere of constant heat flux in an unbounded fluid-saturated porous medium is studied analytically. Transient and steady-state solutions have been obtained for the velocity and temperature fields in the form of series expansions in the Rayleigh number, which is based on the permeability of the porous medium and the heat flux from the sphere. All discussions are based on the assumptions that the flow is governed by Darcy’s law and that the thermal Rayleigh number is small.