Active control of oscillatory thermocapillary flow was applied in an open cylindrical container filled with silicone oil. Thermocapillary convection was driven by imposing a radial temperature gradient on a flat free surface. The control was realized by locally heating the surface at a single position using the local temperature signal at a different position fed back through a simple algorithm. Significant attenuation of the oscillation was achieved in a wide range of supercritical Marangoni numbers, with the best performance in the weakly non-linear regime. Simultaneously measuring the temperature oscillation at two positions gives us a good insight in how the control influences the whole temperature field on the free surface. Quantitative analysis was done to characterize the optimal feedback amplification and the required power.