An approximate method for determining the convective cooling requirement in the laminar-boundary-layer region of a body of revolution in high-speed flight was developed and applied to an example body. The cooling requirement for the example body was determined as a function of Mach number, altitude, size, and a surface-temperature parameter. The maximum value of Mach number considered was 3.0 and the altitudes considered were those within the lower constant-temperature region of the atmosphere (40,000 to 120,000 ft). The extent of the laminar boundary layer was determined approximately at each condition as a function of the variables considered.