Energy conservation and carbon reduction are essential for achieving carbon peaking and neutrality, as well as advancing the green transformation of the economy and society. This research examines the energy-efficient distributed blocked flowshop scheduling problem with heterogeneous factories (EEDBFSP-HF), which aims to simultaneously minimize makespan and total energy consumption (TEC). To tackle the issue, a hybrid multi-objective variable-scale iterated greedy algorithm (HMOVIG) is developed. The algorithm incorporates several customized strategies to enhance solution quality and optimization efficiency. An elite selection strategy is employed to reserve high-quality individuals from the initial population. To promote population diversity and prevent premature convergence, a factory-aware crossover operator and a dynamic destruction intensity strategy are designed. Additionally, a problem-specific energy-saving heuristic is applied to lower TEC. A speedup-based deep local search is further integrated to refine solutions. Numerical experiments validate that HMOVIG consistently surpasses state-of-the-art algorithms in terms of scheduling effectiveness and solution quality.