Self-propulsion of liquid marbles filled with sulfuric acid and coated with hydrophobic fluorosilica powder on a water surface is reported. The prolonged self-propulsion of marbles occurs over a couple of minutes with a typical velocity of the center of mass of the marble being v(cm) similar to 0.01 m/s. The shell of the marble is not uniform, resulting in the asymmetric absorption of water by a marble, giving rise to the nonuniform thermal field within its volume. The maximum temperature reached at the liquid marble surface was 70 degrees C. The self-propelled marble increased its mass by one-third during the course of its motion. The increase in mass followed by the marbles' heating is due to the adsorption of water vapor by their surface, which is permeable to gases. This gives rise to an exothermic chemical reaction, which in turn gives rise to Marangoni thermo-capillary flow driving the marble. Thermo-physical analysis of the problem is presented. The role of soluto-capillary flow in self-propulsion is negligible.