In this study, a numerical investigation of the perturbation evolution in a Mach 6 flat-plate boundary layer with a local heating or cooling strip is presented. The position of the temperature strip is varied while the strip length is constant and approximated to the boundary-layer thickness. Simulations are based on a time-accurate integration of the compressible Navier-Stokes equations, with a small disturbance of fixed frequency triggered via periodic suction-blowing at the plate leading edge. The stability characteristics of the hypersonic boundary layer are interpreted by spatial linear stability theory (LST). The results indicate that the relative location of a local heating/cooling strip and the synchronization point significantly affect Mode S. With respect to the heating-strip cases, the unstable mode is amplified when a heating strip is located upstream of the synchronization point, and the effect is reversed if the heating strip is placed downstream. In a manner opposite to the local heating effect, placing a narrow cooling strip upstream of the synchronization point stabilizes mode S, while the effect is reversed if the cooling strip is put downstream of the synchronization point. Different from previous stability studies on roughness and porous wall, the location of the synchronization point is not fixed, and this is mainly caused by the change to the phase speed of Mode F. The results suggest that an efficient way to stabilize the boundary layer is to put a narrow cooling strip further upstream of the synchronization point, or put a narrow heating strip downstream of the synchronization point. (C) 2018 Elsevier Ltd. All rights reserved.