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 approach cost-optimises the portfolio of heating technologies, including Combined Heat and Power (CHP) and polygeneration systems, large-scale heat pumps (HPs), gas boilers and thermal energy storage (TES). It is implemented as a mixed-integer linear programming (MILP) optimisation model that minimises net cost of heat supply, taking into account investment and operation cost of heat supply and storage options as well as the impact of local and wider interactions with the electricity system.