In this paper we propose a new idea of the use of simulated annealing method to estimate the good value of the minimum distance of linear block codes which remains an open problem and cannot be solved by classical methods because it is in general a NP-hard problem. The main points of the idea is to define in the first hand a new mechanism of moving the search in different regions of solution space by using so called degeneration of energy, notion comes from statistical physics for particles, and in the second hand a new perturbations scheme and acceptance rules to search nearby neighborhoods. To illustrate quality of the proposed approach, we validate the algorithm for some linear codes which the minimum distance is known, and we present the computational experiment results compared to those of previous work which used classic Simulated Annealing algorithm, and those using heuristic techniques such as genetic algorithms and local search algorithms.