This article introduces ME-MLS, an efficient multithreading local search algorithm for solving the multiobjective scheduling problem in heterogeneous computing systems. We consider the minimization of both the makespan and energy consumption objectives. The proposed method follows a fully multiobjective approach, applying a Pareto-based dominance search that is executed in parallel by using several threads. The experimental analysis demonstrates that the new multithreading algorithm outperforms a set of fast and accurate two-phases deterministic heuristics based on the traditional MinMin. The new ME-MLS method is able to achieve significant improvements in both makespan and energy consumption objectives in reduced execution times for a large set of testbed instances, while exhibiting a near linear speedup behavior when using up to 24 threads.