A method for hot-filling and closing a polymer container is disclosed in which one of the closure for the container and the head space area of the container is provided with a hole covered with a hydrophobic air permeable membrane. The container is then filled with a hot liquid and the filled container is closed but for the air permeable component. The filled container is then cooled with the pressure between the interior of the container and the ambient pressure being equalized due to the air permeable membrane. Subsequent to cooling, an air-tight seal is provided over the membrane-covered hole. An associated container and closure cap is also disclosed.