Flexible and responsive demand is key to the decarbonising of energy systems. In this paper, an economic dispatch model of a district heating system, modelled as a linear program, is soft-linked to a so-called flexibility function of end-consumer responses to time-varying heat prices, modelled generically as a set of ordinary differential equations. This linkage allows us to determine the cost savings potential of demand response in order to quantify its role in smart energy systems. Our key contribution is an optimal soft-linking framework for energy system and demand response models, named Frigg. Frigg finds the aforementioned economic potential under consideration of end-consumer behaviour. The dynamics of this behaviour lead to a significant problem complexity and pose computational challenges. Hence, the proposed method decomposes the problem based on backward dynamic programming and solves it efficiently. The framework is to be understood as a generic blue-print for soft-linking demand response and energy system models: It can be applied to a variety of energy systems and sources of demand response as well as other objectives than production cost minimisation. We compute the cost savings in a case study of the district heating system of Ejby, Denmark, under different degrees of demand flexibility. The results are compared with the alternative of investing in heat storage systems. Our results suggest substantial cost savings through demand response. Nevertheless, cost savings from heat storage that is cost-optimal in size exceed those achieved through demand response in the system configurations analysed.