Do European Regions Converge in Carbon Intensity? The Role of Climate-Driven Energy Demand

European regions aim to achieve climate neutrality. This requires the improvement of the carbon efficiency of their energy systems despite the substantial differences in climate conditions and economic structure. This study investigates whether carbon intensity converges across European NUTS-2 regions and examines the role of climate-driven energy demand and spatial interactions in the regional energy transition. Specifically, we use panel data from the period 2000–2024 and investigate the conditional β-convergence based on two-way fixed effects and spatial panel models. The results reveal evidence of conditional convergence, which remains statistically significant after accounting explicitly for spatial dependence, with persistent spatial dependence and point estimates suggesting slower adjustment in regions with initially high carbon intensity. The baseline two-way fixed-effects model implies an annual convergence rate of approximately 13.3%, while spatial specifications that explicitly account for regional dependence yield somewhat lower but comparable rates of approximately 11%. Dynamic-panel robustness checks indicate greater uncertainty regarding the magnitude and statistical precision of the convergence relationship. Climate-driven energy demand and industrial structure are significantly associated with annual carbon-intensity growth. Spatial panel models provide additional evidence of conditional convergence and reveal significant spatial dependence, while the total association between climate-driven energy demand and carbon-intensity growth remains positive across alternative spatial specifications. These findings highlight the importance of place-based energy transition policies that account for regional heterogeneity and spatial dependence in regional decarbonization dynamics.