We perform a molecular dynamics computer simulation of a heat engine model to study how the engine size difference affects its performance. Upon tactically increasing the size of the model anisotropically, we determine that there exists an optimum size at which the model attains the maximum power for the shortest working period. This optimum size locates between the ballistic heat transport region and the diffusive heat transport one. We also study the size dependence of the efficiency at the maximum power. Interestingly, we find that the efficiency at the maximum power around the optimum size attains a value that has been proposed as a universal upper bound, and it even begins to exceed the bound as the size further increases. We explain this behavior of the efficiency at maximum power by using a linear response theory for the heat engine operating under a finite working period, which naturally extends the low-dissipation Carnot cycle model [M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)]. The theory also shows that the efficiency at the maximum power under an extreme condition may reach the Carnot efficiency in principle.© EDP Sciences Società Italiana di Fisica Springer-Verlag 2013.