The axisymmetric deformation and motion of interacting droplets in an imposed temperature gradient is considered using boundary-integral techniques for slow viscous motion. Results showing temporal drop motion, deformations, and separation are presented for equal-viscosity fluids. The focus is on cases when the drops are of equal radii or when the smaller drop trails behind the larger drop. For equal-sized drops, our analysis shows that the motion of a leading drop is retarded while the motion of the trailing one is enchanced compared to the undeformable case. The distance between the centers of equal-sized deformable drops decreases with time. When a small drop follows a large one, two patterns of behavior may exist. For moderate or large initial separation the drops separate. However, if the initial separation is small there is a transient period in which the separation distance initially decreases and only afterward the drops separate. This behavior stems from the multiple time scales that exist in the system.