High-intensity, short-pulse laser radiation incident on the free surface of an absorbing dielectric liquid results in heating that can alter the liquid surface tension, causing Marangoni convection. This flow can dominate the transport of thermal energy in the liquid. In this work, both a scaling analysis and a full numerical simulation of the governing equations are performed. A thermal mechanism is proposed as the driving force for these flows. The dependence on beam size and temperature increase in the liquid is investigated, with good agreement found among the scaling analysis, numerical simulations and experimental data obtained from a previous study. The importance of natural convection and thermal conduction on the fluid-thermal transport was assessed numerically, with both found to be negligible for this liquid-laser system. Velocity and temperature profiles at the liquid surface are also discussed.