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A solution of a variational problem of a slender body with a minimum total radiative heat flux, moving in a gas with a constant velocity, is constructed. It is found that there are three types of the transverse contour of the optimum body: a circumference, a star‐shaped contour, and a contour consisting of circle arcs and sectors of straight lines. The radiation parameter affects only the shape of the longitudinal contour and does not affect the optimum shape of the transverse contour. It is shown that the use of optimum spatial bodies allows a significant (more than 50%( decrease in the radiative heat flux to the body surface as compared to bodies of revolution with similar geometric characteristics.