  A microcanonical treatment of Hagedorn systems, i.e. finite mass hadronic
resonances with an exponential mass spectrum controlled by the Hagedorn
temperature $T_H$, is performed. We show that, in the absence of any
restrictions, a Hagedorn system is a perfect thermostat, i.e. it imparts its
temperature $T_H$ to any other system in thermal contact with it. We study the
thermodynamic effects of the lower mass cut-off in the Hagedorn mass spectrum.
We show that in the presence of a single Hagedorn resonance the temperature of
any number of $N_B$ Boltzmann particles differs only slightly from $T_H$ up to
the kinematically allowed limit $N_B^{kin}$. For $N_B > N_B^{kin}$ however, the
low mass cut-off leads to a decrease of the temperature as $N_B$ grows. The
properties of Hagedorn thermostats naturally explain a single value of
hadronization temperature observed in elementary particle collisions at high
energies and lead to some experimental predictions.
