If the free liquid-gas interface of a liquid in a rectangular Container is subjected to a temperature gra-dient the shear stress on the free liquid surface being temperature dependent transmits by viscous traction a thermo-capillary convection into the bulk of the liquid. For constant temperature T 1 at one wall and T 2 at the other a steady Marangoni convection takes place while for time-oscillatory temperatures of the walls a time-dependent thermo-capillary convection appears, which will create wave patterns on the free liquid surface. They shall, depending on the forcing frequency of the temperature, exhibit resonance peaks. The velocity distribution, the response magnitude inside the Container, the forced free surface displacement and the influence of the Prandtl number have been investigated.