Energy transition through the phase-in of renewables is a crucial pathway for sustainable development. The deployment of renewable energy is increasingly influenced by a country's underlying economic structure and capabilities, captured by economic complexity. This study examines the dynamic and heterogeneous effects of multidimensional economic complexity on renewable energy development. Panel data from 69 countries/regions during 1999-2021 are analyzed using Quantile Regression for Panel Data to investigate the non-linear effects of the multidimensional economic complexity index (ECI) on energy transition and cross-country heterogeneity. The results indicate that trade complexity (trade ECI) hinders energy transition, with the strongest inhibitory effect observed in developed regions. Technology complexity (technology ECI) is found to facilitate energy transition, and this positive effect is strongest in developed regions. Research complexity (research ECI) exhibits a shifting trend, initially negative and subsequently positive, as the quartile of energy structure increases. The robustness tests further confirm the baseline findings. Furthermore, threshold analyses reveal that the negative effect of trade ECI emerges only when industrial structure exceeds a critical value, the positive effect of technology ECI appears after green innovation exceeds its threshold, and the positive influence of research ECI occurs once research and development (R&D) expenditure exceeds the corresponding threshold. This study contributes to the literature by constructing a multidimensional framework of economic complexity, highlighting cross-country heterogeneity between developed and developing economies, and identifying the threshold conditions under which multidimensional ECI either promotes or impedes the transition toward renewable energy.