The enzyme, found in metazoa, methylates a dimethylated L-lysine36 residue of histone H3 (H3K36), which has been methylated previously by EC 2.1.1.357, [histone H3]-lysine36 N-dimethyltransferase. The homologous enzyme from yeast catalyses all three methylations (see EC 2.1.1.359, [histone H3]-lysine36 N-trimethyltransferase).