The flow at different angles of attack past a spherically blunted cone, the spherical and conical parts of which are made of different materials is considered. It is shown theoretically that the manufacture of the side surface of such a body from a highly thermally conductive material provides heat removal from its spherical part, which experiences maximum thermal loads and, accordingly, a decrease in the maximum body temperatures in this area. Dimensionless expressions are obtained for estimating the decrease in the maximum temperatures of a conical body in the area of its spherical bluntness, when the body is immersed in a flow at different angles of attack, by choosing the geometry of the body and materials that have the necessary thermophysical characteristics to cover it.