Temperature-actuated valves, devices including temperature-actuated valves, and related methods are described. In an embodiment, the temperature-actuated valve includes a heat-shrink film defining a perforation extending at least partially in a first direction. In an embodiment, the temperature-actuated valve is configured to open when a portion of the heat-shrink film including the perforation is heated above a threshold temperature to contract the heat-shrink film along a second direction perpendicular to the first direction to define an aperture, in an open configuration, providing a fluid a path through the heat-shrink film. In an embodiment, the temperature-actuated valve includes a leakage-mitigation feature configured to limit fluid flow through the perforation when the valve is in a closed configuration.