Tolerance allocation is a key tool to reach a product design with minimum cost and maximum performance. Since the thermal effects can cause the dimensional and geometrical variations in the components of mechanical assemblies, the tolerance allocation may be inefficient in the optimal tolerance design at the nominal conditions without including the thermal impacts. In this paper, a new optimal tolerance design of mechanical assemblies with the thermal effects is proposed. According to the proposed method, the tolerance allocation procedure is modeled as a multi-objective optimization problem. The functional objective, the manufacturing cost, and the quality loss function are considered as the corresponding objectives multi-objective optimal tolerance design problem. Using the computational results from the finite element simulations and based on the Artificial Neural Network (ANN) method, the design function as functional objective can be modeled. The optimal tolerance design problem in a multi-objective optimization form can be solved using Non-dominated Sorting Genetic Algorithm-II (NSAGA II). The Pareto optimal front (POF) of the proposed multi-objective optimization problem can be obtained. Then, the optimal tolerancs are selected from the POF by the TOPSIS decision-making method. Finally, to illustrate efficiency of the proposed method and to verify it, a case study under various temperature conditions is considered and computational results are compared and discussed.