We demonstrate experimentally control over tubule growth in giant unilamellar vesicles with liquid-liquid phase coexistence, using a thermal gradient to redistribute lipid phase domains on the membrane. As studied previously, the domains of the less abundant phase always partition towards hotter temperatures, depleting the cold side of the vesicle of domains. We couple this mechanism of domain migration with the inclusion of negative-curvature lipids within the membrane, resulting in control of tubule growth direction towards the high temperature. Control of composition determines the interior/exterior growth of tubules, whereas the thermal gradient regulates the length of the tubule relative to the vesicle radius. Maintaining lipid membranes under non-equilibrium conditions, such as thermal gradients, allows the creation of thermally-oriented protrusions, which could be a key step towards developing functional materials or artificial tissues. Interconnected vesicle compartments or ejected daughter vesicles as transport intermediaries towards hot/cold, are just two possibilities.