A "detailed" model of a heat emitter in hot water circulation has been developed considering, two phases (liquid and metal), the non linear heat transfer and the enthalpy transport by the fluid. A reduced order state model ( order two or three) has been then formed, linearising the initial "detailed" model and using a model reduction technique developed in our laboratory which is especially based on modal analysis. The simulated results from both the models for a step input of the inlet temperature have been presented and discussed. The extension of the work in order to identify the parameters of the reduced order state model has been highlighted and further possibilities have been discussed. Finally, this study should be able to define an optimum methodology for the experimental characterisation of fluid circulation emitting devices.