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We discuss the thermodynamic limit in the canonical area ensemble usedin loop quantum gravity to model quantum black holes. The computationof the thermodynamic limit is the rigorous way to obtain a smooth entropyfrom the counting entropy given by a direct determination of the number ofmicrostates compatible with macroscopic quantities (the energy in standardstatistical mechanics or the area in the framework presented here). As wewill show in specific examples the leading behavior of the smoothed entropyfor large horizon areas is the same as the counting entropy but the subleadingcontributions differ. This is important because these corrections determine the concavity or convexity of the entropy as a function of the area.