Numerical study of the concept of active control of growing disturbances in an unstable compressible flow by time-periodic, localized surface heating is presented. The simulations are calculated by a fourth-orderaccurate solution of the compressible, laminar Navier-Stokes equations. Fourth-order accuracy is particularly important for this problem because the solution must be computed over many wavelengths. The numerical results demonstrate the growth of an initially small fluctuation into the nonlinear regime where a local breakdown into smaller scale disturbances can be observed. It is shown that periodic surface heating over a small strip can reduce the growth of the fluctuation provided that the phase of the heating current is properly chosen.