Energy poverty is an increasingly important issue. While vulnerable households are especially at risk in the energy transition, energy poverty effects of the transition are unknown. In Delft, a district heating network based on geothermal energy is planned. The distributive justice aspects of heat networks in the heating transition remain largely unexplored. In this master's thesis, an agent-based model is developed to explore inequalities in energy poverty and access to energy that might arise from the switch to a heat network. The thesis aims to explore the scenarios in which these inequalities can occur and for what types of households, and to determine policy interventions that contribute to a just and inclusive heat network. The extent and distribution of energy poverty and heat network access was explored in multiple energy price contexts, in combination with the following interventions: lower energy tax for gas use below average use and high energy tax for gas use above average use; vouchers to cover upfront costs of heat network connection; renovation of dwellings with poor energetic quality; and awareness campaigns to reduce energy use. The results show that the current district heating pricing structure increases inequality. These costs should be shifted from the high fixed costs to the variable costs to reduce energy poverty in households with low energy consumption. In addition, it was found that building renovation could decrease inequality and energy poverty. Recommendations are made for policy, research and the development of new energy poverty indicators to reduce energy poverty and inequality in the energy transition.