The temperature distribution in an ellipsoidal liquid inclusion in a soluble solid, with a constant gradient far away from the liquid, and the movement of the liquid inclusion as a whole, which results as a consequence, are investigated. Since the solid is soluble and its concentration in solution is temperature dependent, any temperature variation in the liquid induces a concentration variation, which will transfer mass by diffusion, eroding the wall where the temperature is high and depositing solid material at the wall where the temperature is lower. This erosion or deposition will cause the liquid inclusion to move, and will, through absorption or release of latent heat, in turn affect the temperature distribution. From the result obtained for the general ellipsoid, specific results for prolate and oblate ellipsoids of revolution, the sphere, and circular and elliptic cylinders are obtained.