Some methods of control over the thermal regimes realized in a supersonic flow past a conic body with a nose blunted over a sphere were numerically investigated with account of complicating factors. The solution of the problem on the heat and mass transfer in the boundary layer on the surface of this body in the conjugate formulation made it possible to estimate the influence of the nonisothermality of the surface of the body on the characteristics of the indicated transfer. The influence of the rotation of such a body made of composite materials on the heat exchange in the flow over it was determined.