The author studies the linear stage of short-wave Görtler vortices near a concave surface in the regime of weak hypersonic viscous-inviscid interaction at high Reynolds and Görtler numbers. It is assumed that the gas is perfect and the viscosity is a linear function of the enthalpy. It is found that neutral vortices are located near the surface if the latter is at zero temperature. When the surface is heated, the vortices move away from it, whereas newly generated vortices are located near the surface. The author shows that the growth rate of vortices has a maximum, and the heating has a stabilizing effect on them. One of the methods of analysis used in the article, is the introduction of new variables and the asymptotic analysis of streamfunctions in the disturbed region.