Combined thermocapillary and natural convection in rectangular containers is investigated experimentally and theoretically. The fluid is heated by a thin wire placed along the free surface. In the parametric range investigated herein, buoyancy alters the thermocapillary flow significantly. The flow field is confined to a relatively small region near the free surface due to thermal stratification. The vertical dimension of the flow cell is determined by a scaling analysis, and the scaling law is shown to agree well with the results from the numerical simulations. The experiment shows that the steady two-dimensional flow field becomes oscillatory and three-dimensional beyond a certain temperature difference. The oscillatory flow field is described based on a flow visualization and temperature measurement, The critical temperature difference for the onset of oscillations is determined under various conditions. It is discussed that the flow becomes oscillatory when the convection in the flow cell becomes sufficiently large. A parameter is derived to represent this convection including the effect of stratification, which is shown to correlate the experimentally determined critical conditions well.