while (my $uniqueseq = $stream->next_seq()) { 
               push @oligomers, $uniqueseq->seq; }
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Instead of expanding all possible combinations into an array that you then iterate over, why not directly call tm_Base_Stacking(...) (or tm_NNH() for that matter(?)) in that loop?

That should at least get rid of the memory problem (unless the Bio::Tools::IUPAC iterator internally pre-expands the set itself), although the runtime problem would likely still persist...