The governing equations for momentum and energy transport have been solved for the thermocapillary flow in a differentially heated square cavity. The fluid was assumed to contain a surface active impurity such that the surface tension was a quadratic function of the temperature where the maximum surface tension occurs at the mean cavity temperature A Prandtl number of 0.1 was used because the primary interest here is for liquid metals. For low Marangoni numbers the flow was steady, stable and symmetric about the center vertical plane and consisted of two opposing vortices. For Marangoni numbers above 1200 the flow, given an initial disturbance, was oscillatory and in a periodic steady state.