Temperature sequences are formulated as a complete method of categorizing the feasible distillation boundary maps (DBMs) for ternary systems which commonly have unique binary and ternary azeotropes. DBMs are simplified versions of residue curve maps. The method requires the boiling temperatures at system pressure of pure components and azeotropes, if they exist. Seven position numbers are assigned to the pure components (three) and azeotropes (three binary, one ternary). The boiling temperatures are sorted to rank the position numbers. The temperature sequence is defined as the ranking of position numbers. The position numbers of missing azeotropes are excluded from the sequence. An algorithm searches all possible temperature sequences for feasible DBMs. The result is a complete listing of 125 DBMs, 307 temperature sequences, and 382 [temperature sequence, DBM] pairs. Lookup tables simplify the procedure for finding the DBM(s) for a temperature sequence or finding the temperature sequences for a DBM. Example applications are presented for applying the technique in the initial screening for distillation system synthesis.