We explore the thermal field related to the self-propulsion of floating liquid marbles filled with aqueous ethanol. Cherenkov-like thermal waves arising from self-propulsion are registered. The opening angle of the thermal field Cherenkov triangle is governed by the inter-relation between the velocity of self-propulsion and the phase velocity of the capillary waves. The self-propulsion is driven by soluto-capillarity accompanied by thermo-capillarity. A semiquantitative analysis of the effect is presented. The empirical selection rule for capillary waves responsible for the mass, momentum, and heat transfer is outlined. The soluto-capillarity leads to much stronger spatial variations of the surface tension than the thermo-capillarity.