Decarbonisation of the heating and cooling sector is critical for achieving long-term energy and climate change objectives. Closer integration between heating/cooling and electricity systems can provide additional flexibility required to support the integration of variable renewables and other low-carbon energy sources. This paper proposes a framework for identifying cost-efficient solutions for supplying district heating systems within both operation and investment timescales, while considering local and national-level interactions between heat and electricity infrastructures. The proposed optimisation model minimises the levelised cost of a portfolio of heating technologies, and in particular Combined Heat and Power (CHP) and polygeneration systems, centralised heat pumps (HPs), centralised boilers and thermal energy storage (TES). A number of illustrative case studies are presented, quantifying the impact of renewable penetration, electricity price volatility, local grid constraints and local emission targets on optimal planning and operation of heat production assets. The sensitivity analysis demonstrates that the cost-optimal TES capacity could increase by 41–134% in order to manage a constraint in the local electricity grid, while in systems with higher RES penetration reflected in higher electricity price volatility it may be optimal to increase the TES capacity by 50–66% compared to constant prices, allowing centralised electric HP technologies to divert excess electricity produced by intermittent renewable generators to the heating sector. This confirms the importance of reflecting the whole-system value of heating technologies in the underlying cost-benefit analysis of heat networks.