Compound droplets impacting on a solid surface appear in many natural and industrial processes. In some practical or engineering applications, the droplet needs to be levitated and then transported without friction or contamination with a surface. When the droplet hits a surface, it can rebound due to the impact energy, however, it then falls down on the surface. To stabilize the droplet above a surface, it is necessary to use external sources induced by, e.g., electricity, magneticity, thermocapillary action and so on. We present here a numerical investigation of the behaviors of a compound droplet impacting on a non-wetting wall under the excitation of a temperature gradient. To show the dynamics of the compound droplet, various parameters are studied, including the Marangoni number Ma (varied in the range of 50–350), the inner-to-outer volume ratio V_io (varied in the range of 0.027–0.512), the inner-to-outer interfacial tension ratio σ_io (varied in the range of 0.6–4.8), the Bond number Bo (varied in the range of 0.18–5.6), the Weber number (varied in the range of 0.32–1.4), and the Reynolds number (varied in the range of 10.0–40.0). We find that the temperature gradient has a strong influence on the droplet after impacting the wall. It assists the droplet to rebound and stabilize its position above the wall. However, in some cases, after rebounding to a certain height, the droplet then deposits again on the wall. The behavior of the droplet strongly depends on the dimensionless parameters. It is found that as the value of Ma is smaller than 150, the droplet cannot rebound, while it stays completely above the wall for Ma ≥ 250. When Ma is between 150 and 250, the droplet rebounds to a certain height and then settles on the wall. The droplet also rebounds and stays above the wall for Bo < 1.0. In addition, decreasing V_io, σ_io, or Re tends to enhance the droplet rebound. In contrast, increasing the Weber number beyond the critical value (We = 0.64) increases the stable rebound height. The effects of these parameters on the rebound heights and residence time are also investigated.