The combination of buoyancy and thermocapillarity can cause a flow that impedes or alters the motion of a bubble in reduced gravity. In analyzing such a flow, it is important to account for the dynamics occurring on the surface of the bubble. A first-order solution to the governing equations of motion and energy is presented for small Reynolds numbers. This solution provides the means to determine the terminal velocity, the direction of motion, the external flow and temperature fields of a bubble. Its features explicitly account for all gravity levels by using a Bond number and consider the negative variation of the surface tension with temperature. Streamline patterns outside the bubble are computed to obtain an overall picture of the flow over the range 0⩽Re⩽20. The results of the analysis compare the homogeneous to the first-order solutions by illustrating differences to five unique flow regimes as the Bond number changes from small to very large values, i.e., from thermocapillary to gravity dominated ...