Solving energy-saving distributed heterogeneous flexible job shop scheduling problem (ES-DHFJSP) aims to enhance industrial production efficiency while minimizing energy consumption. State-of-the-art co-evolutionary algorithms have emerged as effective approaches for addressing ES-DHFJSP. However, existing methodologies demonstrate compromised convergence rates and excessive computational overhead when confronted with vast search spaces. In this work, we propose a novel solution space transformation-guided co-evolution algorithm (SSTCE) to overcome this limitation. In SSTCE, we first establish an inter-job similarity metric and incorporate constrained hierarchical clustering with optimal leaf ordering (CHC-OLO) to generate clustered job sets, which are subsequently utilized for population initialization that achieves a favorable balance between convergence and diversity. To enhance search capability in expansive solution spaces, we devise a dynamic solution space transformation mechanism that effectively reduces inefficient searches within the algorithm. Furthermore, we develop tailored local search strategies leveraging domain-specific knowledge of DHFJSP properties. Extensive experimental evaluations across 20 benchmark instances demonstrate that SSTCE significantly outperforms existing evolutionary algorithms in solving ES-DHFJSP.