District heating is a network of pipes through which heat is delivered from a centralised source. It is expected to play an important role in the decarbonisation of the energy sector in the coming years. In district heating, heat is traditionally generated through fossil fuels, often with combined heat and power (CHP) units. However, increasingly, waste heat is being used as a low carbon alternative, either directly or, for low temperature sources, via a heat pump. The design of district heating often has competing objectives: the need for inexpensive energy and meeting low carbon targets. In addition, the planning of district heating schemes is subject to multiple sources of uncertainty such as variability in heat demand and energy prices. This paper proposes a decision support tool to analyse and compare system designs for district heating under uncertainty using stochastic ordering (dominance). Contrary to traditional uncertainty metrics that provide statistical summaries and impose total ordering, stochastic ordering is a partial ordering and operates with full probability distributions. In our analysis, we apply the orderings in the mean and dispersion to the waste heat recovery problem in Brunswick, Germany.