Optimal steady perturbations in the boundary layer over a sphere are considered within the scope of the parabolized stability equations (PSE). The flow parameters at the edge of the boundary layer correspond to a high-speed free-stream flow of a calorically perfect gas, and the boundary layer velocity and temperature profiles are obtained using the local-similarity approximation. The governing PSE equations are derived from the linearized Navier-Stokes equations in spherical coordinates within the scope of the concept of optimal perturbations as streamwise vortices. Analysis of the transient growth phenomenon revealed that an increase of the sphere radius leads to an increase of the transient growth, and that the transient growth effect is stronger in the vicinity of the stagnation point. Similarly to previous results for compressible boundary layers, cooling of the wall destabilizes the boundary layer flow.