Domain migration is observed on the surface of ternary giant unilamellar vesicles held in a temperature gradient in conditions where they exhibit coexistence of two liquid phases. The migration localizes domains to the hot side of the vesicle, regardless of whether the domain is composed of the more ordered or disordered phase and regardless of the proximity to chamber boundaries. The distribution of domains is explored for domains that coarsen and for those held apart due to long-range repulsions. After considering several potential mechanisms for the migration, including the temperature preferences for each lipid, the favored curvature for each phase, and the thermophoretic flow around the vesicle, we show that observations are consistent with the general process of minimizing the system's line tension energy, because of the lowering of line interface energy closer to mixing. DNA strands, attached to the lipid bilayer with cholesterol anchors, act as an exemplar "cargo," demonstrating that the directed motion of domains toward higher temperatures provides a route to relocate species that preferentially reside in the domains.vesicles | thermophoresis | DNA | lipid bilayers | lipid phase separation G iant unilamellar vesicles (GUVs) provide a simplified model for studying various aspects of biological membranes. GUVs of a saturated lipid, an unsaturated lipid, and a sterol can form domains of coexisting liquid phases below a critical transition temperature, Tt. Domains diffuse on the surface of the vesicle with a diffusion coefficient that depends on the domain size and the membrane viscosity (1). The domain morphology is strongly linked to the temperature and composition of the membrane (2-4) and also the membrane tension (5). GUVs have been observed to form a range of shapes (6-9) and domain morphologies (2, 10), including modulated phases (11). However, to minimize their edge length, liquid phase domains most commonly form circular patches and coarsen to reduce the overall line energy over the membrane. "Normal" coarsening can occur by collision and coalescence of domains because of their diffusive motion (12, 13) or by Ostwald ripening (14). In practice, membrane curvature adds other degrees of freedom and provides another route to minimize the free energy via domain budding (15-17). Domains of the phase with a lower bending modulus may dimple from the surface of the vesicle. Repulsive interactions (associated with curvature of the membrane between domains) keep dimpled domains apart and cause a reduction in the rate of coalescence ("hindered" coarsening) (13,18).The behavior of domains in liquid-ordered (Lo)/liquid-disordered (L d ) phase coexistence has been explored in equilibrium and during coarsening (12). Such studies include the fluctuations in the domain boundary observed near Tt (19) and the dependence of Tt on the membrane composition (4). However, these studies look only at a fixed temperature across a domain. Although osmotic gradients have been explored to induce shape changes in vesicles (9), t...