Comparisons are made of the one-dimensional and two-dimensional centerline temperature profiles and heat lost ratios for a radial fin of uniform thickness on a pipe. Effects of the Blot number fin thickness, and size ratio (ratio of radial distances of the tip and root) are investigated. In particular the more restrictive two-dimensional results as to the usefulness of the fin are demonstrated. Further, the distortion of the two-dimension temperature profile for intermediate values of the Blot number exhibit regions where waste of material in this shape of fin occurs. Finally, information is presented that relates the fin size (radially) and the Blot number magnitude for which the fin is beneficial.