The equations of the compressible laminar boundary layer for the windward streamline in the plane of symmetry (most windward streamline) of a yawed cone are presented. Since, for a Prandtl number of 1, the energy equation resembles the momentum equation in the meridional direction (along a generator), solutions are obtained for both insulated and cooled surfaces. The heat-transfer rate to this most windward streamline increases significantly with angle of attack. For a surface cooled to absolute zero temperature, the relative increase with angle of attack is about 15 percent less than for an almost insulated surface. A supplementary calculation shows the heat transfer to vary with the Prandtl number, Pr, approximately as Pr to the 0.37 power, while the recovery factor is well estimated by the square root of the Prandtl number.