Transformative actions are crucial across all sectors emitting greenhouse gases. Nonetheless, energy transition research to date displays a notable imbalance, with a larger emphasis on the supply side than on the demand side. The present study addresses this inequity by focusing on residential sector space heating demand, a frequently overlooked energy service that currently contributes substantially to global greenhouse gas emissions. Our primary objective is to pinpoint effective climate policies and space heating strategies that align with the EU’s ambitious targets for emission reduction. We employ the recently developed TIMES-Europe model to conduct a comprehensive analysis of the residential sector’s policy frameworks, technological advancements, and associated costs. This analysis aims to determine the measures necessary to meet ambitious climate objectives within the European context. To achieve this, we formulate four distinct scenarios, each representing varying levels of ambition and collaboration among EU member states, thereby providing insight into the pathways toward achieving these targets. By implementing current intended EU policies on the renovation of dwellings, we project a substantial reduction of at most 850 PJ, or, i.e., a 19% decrease, in yearly energy demand for space heating between 2020 and 2050. In contrast, if the recent pace of dwelling renovation within the EU were to continue, space heating energy savings from renovation would only amount to less than 400 PJ/yr (i.e., a 9% reduction) in the same period. In our more ambitious climate scenarios, phasing out fossil fuels leads to widespread electrification of the European residential sector, and by 2050, electricity from heat pumps and electric boilers accounts for over 68% of the total residential sector space heating demand. The outcomes of our study underline the importance of implementing the currently planned EU policies. We also demonstrate the necessity for collaboration among EU member states in order to attain the common European climate targets under the most effective resource allocation.