We present a local search based algorithm designing DNA short-sequence sets satisfying thermodynamical constraints about minimum free energy (MFE) criteria. In DNA12, Kawashimo et al. propose a dynamic neighborhood search algorithm for the sequence design under hamming distance based constraints, where an efficient search is achieved by dynamically controlling the neighborhood structures. Different from the hamming distance based constraints, the thermodynamical constraints are generally difficult to handle in local-search type algorithms. This is because they require a large number of evaluations of MFE to find an improved solution, but the definition of MFE itself contains time-consuming computation. In this paper, we introduce techniques to reduce such time-consuming evaluations of MFE, by which the proposed dynamic neighborhood search strategy become applicable to the thermodynamical constraints in practice. In computational experiments, our algorithm succeeded in generating better sequence sets for many constraints than exiting methods.