The classical problem of a steady plane laminar plume is revisited. A critical review of the literature reveals unresolved discrepancies between self-similar boundary-layer solutions and measurements. Thus, the two-dimensional natural convection flow over a heated horizontal cylinder, forming a plume above the cylinder, is computed numerically to identify the sources of the discrepancy. The flow is realized in a large enclosure that is four orders of magnitude larger than the cylinder diameter. It is found that even such a large enclosure can significantly alter the plume’s enthalpy and momentum flow. Nevertheless, sufficiently far from the enclosure walls, a reasonable agreement with a classical analytical solution from literature was obtained. Apart from enclosure effects, other possible sources of the long-standing discrepancies between experimental and analytical results include radiation heat transfer and a shift in the plume’s virtual origin due to a diffusion-dominated flow region around the cylinder.