Turbulent boundary-layer heat transfer and skin-friction coefficients were measured on sharp slender cones at a free-stream Mach number of 5.0. Wall-to-stagnation temperature ratios from 0.15 to 0.80 were obtained by precooling or preheating the model. Tests were conducted for a wide range of Reynolds numbers by varying the tunnel supply pressure and temperature, thus providing data for naturally turbulent boundary layers. The experimental results were compared with existing theories which predict convective Stanton number or skin-friction coefficients. These comparisons indicate that the heat-transfer data are best predicted by the Spalding-Chi law and the skin friction by the Sommer-Short reference temperature method. The experimental Reynolds analogy factor is adequately predicted by Colburn's incompressible correlation for wall-to-stagnation temperature ratios above about 0.5. However, for lower wall temperature ratios, the experimental Reynolds analogy factor decreases with decreased temperature ratios in a manner which has not been previously reported. (Author).