An optimisation model for the sustainable design of refrigerated automated storage and retrieval systems is proposed, which takes into account specific features of the food supply chain, such as temperature control. Rack configuration as well as surfaces and volumes of the cold cell are conjointly optimised in order to minimise the total yearly cost of the automated storage facility, introducing energy requirements both for refrigeration and picking operations explicitly, other than investment costs. Crane plus satellite systems are modelled in order to enable deep lane solutions and space savings, as suitable for cold storage. The model allows a deep analysis of the impact of supply chain decision variables, such as the facility location, the storage temperature and the incoming product temperature on costs, energy use and carbon dioxide emissions, so that storage facilities attributes for supply chain design models can be properly assessed to re-optimise the whole cold chain. The design problem is modelled and solved by Constraint Programming in order to easily manage non-linear functions.