Hydrophobic side groups on a stimuli-responsive polymer, encapsulated within a single giant unilamellar vesicle, enable membrane attachment during compartment formation at elevated temperatures. We thermally modulated the vesicle through implementation of an IR laser via an optical fiber, enabling localized directed heating. Polymer-membrane interactions were monitored using confocal imaging techniques as subsequent membrane protrusions occurred and lipid nanotubes formed in response to the polymer hydrogel contraction. These nanotubes, bridging the vesicle membrane to the contracting hydrogel, were retained on the surface of the polymer compartment, where they were transformed into smaller vesicles in a process reminiscent of cellular endocytosis. This development of a synthetic vesicle system containing a stimuli-responsive polymer could lead to a new platform for studying inter/intramembrane transport through lipid nanotubes.