Assessing　and　monitoring　the　green　total　factor　energy　efficiency　(GTFEE)　of　cities　while　considering　technology　heterogeneity　is　crucial　for　the　development　of　energy-conservation　and　emission-reduction　policies.　Considering　that　the　heterogeneity　of　production　technologies　encompasses　several　dimensions,　this　paper　proposes　a　3E3S　(Economy-Environment-Energy-Society-Science-Space)　heterogeneity　framework　and　integrates　it　with　the　improved　meta-frontier　global　SBM-undesirable　to　analyze　GTFEE　and　its　decomposition.　Empirical　analysis　of　cities　in　the　Yellow　River　Basin　of　China　(YRBC)　highlights　the　following:　(1)　The　3E3S　heterogeneity　framework　facilitates　the　classification　of　all　cities　into　three　distinct　groups,　a　finding　that　contrasts　significantly　with　previous　outcomes　documented　in　the　literature　that　relied　solely　on　criteria　such　as　geographic　location.　(2)　The　three　groups　identified　under　the　meta-frontier　exhibit　substantial　energy-saving　potentials　of　24.49%,　35.17%,　and　52.46%,　respectively.　Additionally,　there　are　spatiotemporal　variations　in　GTFEE,　with　cities　located　in　the　central　part　of　YRBC,　particularly　those　in　Shanxi　province,　demonstrating　poor　GTFEE　performance.　(3)　The　decomposition　analysis　of　GTFEE　indicates　that　technological　progress　plays　a　pivotal　role　in　enhancing　GTFEE　on　the　whole,　albeit　with　varying　approaches　for　improving　GTFEE　depending　on　individual　cities.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2024.