Heat-transfer rates were measured on large-angle conical bodies with large half-angles between 50 degrees and 90 degrees, at angles of attack from 0 degrees. The results at 0 degree angle of attack were predicted with Lees' similarity theory, using calculated flow properties at the boundary-layer edge. The calculated flow properties were obtained from Newtonian theory for the 50 degree cone and from a one- or two-strip solution using the method of integral relations for other cones. At 0 degree angle of attack, an increase in cone angle resulted in a decrease in the heating rate over much of the body. However, high heating rates occurred at the shoulder of the both the half-angle = 80 degree and half-angle =90 degree shapes because of local pressure gradients. On the windward side of the cones, the heating rate increased with angle of attack.