Based on the total volume and fin-material volume constraints, a tree-shaped assembly of fins is optimized with entransy dissipation rate minimization, and the dimensionless mean thermal resistance and the corresponding optimal construct are obtained. The results show that the heat conductance performance of the assembly is better as the fraction of fin material increases, thermal conductivity of fin grows smaller, and the heat transfer coefficient of fin over all the exposed surfaces becomes larger. The heat conductance performance of the tree-shaped assembly is not always better with more complexity, and is far better than that of the T-shaped assembly. The optimal constructs corresponding to the minimization of entransy dissipation rate and the minimization of maximum thermal resistance, respectively, are different obviously. For the former, its dimensionless mean thermal resistance is smaller, and the heat conductance performance is much better. (C) 2013 Elsevier Ltd. All rights reserved.