Increasing energy efficiency of buildings by renovation and thermal insulation is widely seen as means to lessen energy demand and to increase thermal comfort. However, costs of renovation and the dangers of displacing low income, energy poor households due to rent increases are generally not addressed in literature on benefits of thermal insulation. In an exemplary manner for a selected case study in Austria this article investigates if reduced energy costs due to thermal insulation can offset rent increases. Results clearly show that this approach will not work for renting households at risk of poverty as their energy consumption mostly is already extremely limited before renovation (prebound effect), thus no further reduction can be expected after renovation as energy poor households tend to use renovation benefits for increased comfort rather than reduced consumption (rebound effect). As a consequence we propose the design of funding schemes to identify and prioritize socio-economic hot spots in housing stock.