Box for products to be kept cold

A portable box defining a space for containing a product, e.g. a frozen or chilled foodstuff, includes an internal compartment (19) for accommodating a cooling means, e.g. dry ice. A lid (16) allows a consumer access to the box. A partition (18) prevents contact between the product (or the consumer's hand) and the cooling means and permits heat transfer by convection. The box is constructed of poorly conductive sheet material (cardboard) and heat entering any side of the box preferably has to pass through at least two thicknesses of the sheet material.