A precisely fabricated, spherical thermal conductivity cell is used to achieve stady, one-dimensional, loss-free radial heat conduction across an annular test specimen. The investigated test specimens are solid, 99% pure n-eicosane paraffin, which are cast in place by using the conductivity cell as a mold. The conductivity is determined as a function of the mean temperature of the specimen, and its sensitivity to a number of parameters is investigated. These include the presence or absence of vacuum during casting, the rate of solidification during casting, the thermal contact between the conductivity cell walls and the test specimen, the temperature difference across the specimen, the experimental site, and the aging of the apparatus and the paraffin. In supplementary experiments, the density of the solid paraffin and its melting temperature are determined. For specimens cast without vacuum, the thermal conductivity is virtually independent of the specimen temperature and of the solidification rate. However, for speciments cast under vacuum, the conductivity is found to be sensitive to the solidification rate, as is the density, and this dependence is attributed to the presence of entrapped gas bubbles. Comparison with the literature shows prior conductivity values for solid n-eicosane to be low, thereby explaining reported deviations between experimental and numerical results for solidification phase change.