A new search space smoothing method is developed for the study aiming at a function-based understanding of the local search approach for heuristic optimization. The algorithm is designed by using the Metropolis algorithm as a local search procedure and is arranged to solve the traveling salesman problem. The schedule for the smoothing parameter and the value of the temperature for the search with the Metropolis algorithm are determined by considering the smoothing-parameter dependence of the specific heat and the temperature dependence of the optimization performance. The resulting algorithm successfully improves the performance of the existing algorithm in combination with the 2-opt local search procedure.