  The self-consistency of a thermodynamical theory for hadronic sys- tems based
on the non-extensive statistics is investigated. We show that it is possible to
obtain a self-consistent theory according to the asymptotic bootstrap principle
if the mass spectrum and the energy density increase q-exponentially. A direct
consequence is the existence of a limiting effective temperature for the
hadronic system. We show that this result is in agreement with experiments.
