The axisymmetric deformation and motion of interacting droplets under the combined influence of the gravitational force and a vertical temperature gradient is considered using boundary-integral techniques for creeping flow. The focus is on the case when the net thermocapillary and buoyancy forces acting on the drops are directed oppositely. When these forces are almost balanced our analysis shows that, though the deformations of the drops are apparently small, their influence on the motion is considerable. For highly deformable drops moving in a gravity field, even a small temperature gradient that almost does not effect the drops velocity may drastically change the deformation pattern and prevent the drops from breakup.