In order to cool a room with a cold night air phase change material, PCM, is stored in an air heat exchanger. During night the PCM crystallises, energy is released. During daytime air is circulated in the unit, energy is absorbed and the indoor air is cooled. The characteristic of PCM is that there is an increase of the specific heat over a limited temperature span. This is the principle that is used in the design of the PCM air heat exchanger unit. The action of a PCM storage unit will act differently depending of the thermal properties of the material. In an ideal material the phase transition occurs at a given temperature. On the market, compounds containing PCM are available which, in order to create a suitable melting temperature, are mixtures of different products. In these materials, the transition from liquid to solid takes place over a temperature span, i.e. the specific heat varies with the temperature. This can be represented by a c(p)(T) curve, specific heat as a function of the temperature. In this paper, the development of a mathematical model of the PCM air heat exchanger is presented. Considerations are taken to different shapes of the cp(T) curve. The mathematical model is verified with measurement on a prototype heat exchanger. The development of the equipment is part of the CRAFT project Changeable Thermal Inertia Dry Enclosures (C-TIDE) the possibility of use of phase change materials integrated into a building is explored.