Transitioning energy systems to renewable sources requires a paradigm shift in system operation: Rather than dispatching central generators to match volatile demand, the demand side must be adjusted flexibly to match renewable generation. Electrified heating is one source of such flexibility, via demand response and heat storage. In energy system analysis, demand response is often modelled as a direct control problem, where central decisions set demand levels. We consider this an over-simplification and propose an update of Frigg: a framework for integrating price-based indirect demand response models in energy system analysis. The update solves many previous shortcomings, such as modelling a larger number of intertemporal constraints. In this paper, Frigg is applied to soft-link plan4EU, a European electricity dispatch model, and the Flexibility Function. Based on this modelling setup, we conduct a case study on the role of power-to-heat demand flexibility, in the form of demand response and heat storage, in the Danish electricity system of 2050. Our results highlight the significance of Denmark as an electricity transit country: We find that power-to-heat demand response offers mild cost savings in the Danish electricity system, mainly through lower-cost electricity imports and higher-cost exports. Similarly, heat storage allows utilisation of the Danish geographical position. Heat storage achieves significantly higher savings than only demand response. Combining heat storage with demand response achieves similar operational savings but lowers heat-storage investment costs, leading to an overall cost reduction of approximately 7% in 2050.