For the conditions obtained in experiments on the interaction of a shock wave with an ionization unstable plasma, a numerical simulation of the impact of a thermally stratified energy source on the shock wave front is performed based on the full Navier-Stokes equations. It has been shown that its curvature, registered in schlieren-images, is associated with a higher temperature of the central layers of the source, and its disappearance is due to the multiple generation of the Richtmayer-Meshkov instabilities, which were obtained in the field of gas density. In addition, it was shown that when the source energy is redistributed into layers, local regions are formed behind the shock wave front with a gas temperature several times higher than the values for a homogeneous source.