Liners for cooking vessels, cooking systems, and methods of making liners for cooking vessels are disclosed. The liner can be a multi-layer liner having a bag-like structure with a closed bottom having a bottom edge, a top opening having first and second top edges, and two sealed sides. The liner can have a first side seal extending along a first end from the top opening toward the bottom edge and a second side seal extending along a second end from the top opening toward the bottom edge. The liner material can include an aluminum foil sheet thermally laminated to a polymer film. The polymer film can include a biaxially-oriented polyethylene terephthalate layer coextruded with an amorphous polyethylene terephthalate sealant layer.