The stability of water droplets migrating in a thermal gradient in a single crystal of KCl was studied as a function of droplet size, droplet shape, droplet velocity and the applied thermal gradient in the solid. Droplet breakdown starts with the growth of protrusions from the rear corners of the droplet and is followed by the release of a thin trailing liquid veil from the rear peripheral edges of the droplet at a somewhat higher thermal gradient. Droplets with a velocity to applied thermal gradient ratio less than 9.4 × 10 −8cm 2/sec°C are stable while droplets with a greater ratio are unstable. This stability criterion is shown to be consistent with the idea that droplets disintegrate when the bulk droplet velocity exceeds the maximum theoretical velocity of droplet edges. The velocity difference arises from the difference between the thermal gradients in the center and the edges of a droplet.