The development of the so-called Görtler vortices in boundary layer flows over a concave surface leads to strong velocity gradients in both wall-normal and spanwise directions. This determines the flow structures to become more prone to secondary instabilities, which prompt to an early transition from laminar to turbulent flow, ultimately increasing the frictional drag. It is possible to circumvent these secondary instabilities by means of passive or active flow control strategies, with sensors and actuators implemented at the wall. In this thesis, the effect of wall cooling and heating on Görtler vortices developing in supersonic and hypersonic boundary layers is investigated from a numerical point of view. The wall temperature is imposed through a ramping function that decreases or increases an upstream base wall temperature in the streamwise direction. The results show that this type of wall cooling or heating has a mild (adverse) effect on the vortex energy, and a more considerable (but beneficial) effect on the wall shear stress.