The results of an experimental study of the influence of local heating/cooling of a blunted cone nose-tip on the development of perturbations in the boundary layer for Mach number M = 6 are presented. A comparative analysis of the pressure-pulsation spectra on the cone surface has been carried out. It is shown that heating/cooling in the boundary layer of an acute cone leads to destabilization/stabilization of the perturbations of the second mode. For blunted cones, the opposite effect has been observed: heating leads to weak stabilization of disturbances, and cooling leads to destabilization. This effect is enhanced by increasing the bluntness radius of the cone nose-tip.