This paper investigates how using heat pumps for domestic heating would impact fuel poverty and social inequality. The analysis integrates a geospatial description of climate observations, gas and electricity infrastructure, energy consumption and fuel poverty from the base world of a Universal Digital Twin based on the World Avatar knowledge graph. Historic temperature data were used to estimate the temporal and geospatial variation of the performance of air source heat pumps in the UK. The corresponding change in gas and electricity consumption that could be achieved using heat pumps instead of gas for domestic heating was estimated. The geospatial impact of the heat pumps was assessed in terms of CO2 savings, and their effect on fuel cost and fuel poverty. Whilst heat pumps would reduce emissions, it is predicted that they would increase fuel costs. It was shown that both local and regional areas of high fuel poverty would experience some of the largest increases in fuel cost. This illustrates the potential for the transition to sustainable heating to exacerbate social inequality. The analysis suggests that existing regional inequalities will increase, and that it comes down to a political choice between investments to support the most effective use of heat pumps, and delayed investments to counter social inequality. The ability of the World Avatar to integrate the models and data necessary to perform this type of holistic analysis provides a means to generate actionable information, for example, to enable local policy interventions to address the tension between social and environmental goals.