We present general techniques to speed up local search type algorithms for designing DNA sequences which satisfy thermodynamical constraints based on the minimum free energy (MFE) criteria. MFE based constraints are generally difficult to handle in local search type algorithms, since these algorithms typically require a large number of time-consuming calculations of MFE to find an improved solution. In this paper, we introduce general techniques to reduce such calculations of MFE. The ideas are based on the reuse of MFE computations and fast approximation of MFE, both of which fit the nature of local search type algorithms. In computational experiments, our techniques succeeded in speeding up typical local search type algorithms without degenerating the original performance of the algorithms.