A cooler for breast milk or other liquids is disclosed. The cooler comprehends an interior pocket adapted to receive lactation accessories that a user wishes to be cooled. The interior pocket can be adapted to be positioned in a variety of locations within the cooler to enhance or restrict the efficiency of thermal transmission between the contents of the pocket and a cooling element located within the cooler. Also disclosed is a sensor that can be associated with the pocket. The sensor can provide a temperature output to an external device or a display in or on the container delineating a temperature within the cooler.