In this paper we study the partition function of a macroscopic hadron system with two models. In one model the mathematical fireball appears as a fundamental particle in a Boltzmann ideal gas occupying a volumeV. In a second model the macroscopic volumeV is divided in noninteracting boxes of volumeV0, each one containing an interacting-pion gas. Both cases show the same limiting temperatureT* produced by the bootstrap equation, although far fromT* they represent different thermodynamic systems.