Conjugate heat transfer by steady laminar natural convection from an isothermal circular cylinder with one infinitely long vertical plate fin has been studied by a finite-difference numerical procedure. Interactions between the fin and cylinder boundary layers are determined through the elliptic nature of the solution technique. Heat transfer from both the fin and the cylinder is less than predicted, disregarding the complex interactions. A fin of low conductance reduces the total heat transfer below the free-cylinder value. Fins of large conductance enhance the total heat transfer by a few percent. Heat transfer correlations have been developed to predict local and total heat transfer rates for both the fin and the cylinder as a function of the three governing dimensionless parameters: Rayleigh number, Prandtl number, and fin conduction parameter.