A new mapping heuristic is developed, based on the recently proposed Mean Field Annealing (MFA) algorithm. An efficient implementation scheme, which decreases the complexity of the proposed algorithm by asymptotical factors, is also given. Performance of the proposed MFA algorithm is evaluated in comparison with two well-known heuristics: Simulated Annealing and Kernighan-Lin. Results of the experiments indicate that MFA can be used as an alternative heuristic for solving the mapping problem. The inherent parallelism of the MFA is exploited by designing an efficient parallel algorithm for the proposed MFA heuristic.