Liquid metal in a closed container made of dissimilar metal under a magnetic field is, in general, set into motion by thermoelectric effects if the interfacial temperature is nonuniform, a situation likely to occur in fusion reactor blankets owing to the high thermoelectric power of lithium. The paper sets out the general problem for the case where the field is uniform and so strong that inertial and viscous effects are negligible and where the container wall thickness is small and uniform. Extended cylindrical portions of interface, parallel to the magnetic field, are excluded. Particular attention is paid to containers which are axisymmetric about the field direction and several solutions are found for the case of a spherical container. Many of these imply drastic changes in the total heat transport as compared with pure conduction in the static liquid.