  We investigate the possibility of describing the thermal system with
different temperatures for a black hole with multiple horizons. The black hole
with two horizons such as Schwarzschild-de Sitter black hole corresponds to two
thermal systems with generically different temperatures. Then, it is not
suitable to describe these systems with equilibrium thermodynamics
corresponding to Gibbs-Boltzmann kinetic theory. In the present work, we
investigate such thermal systems by using hydrostatic equilibrium
thermodynamics. Assuming that the gas between the horizons obeys the Tsallis
statistical mechanics, we found that it is possible to obtain the temperature
gradient for the classical gas. Interestingly, the gas behaves as classical gas
near the horizon and behaves like quantum gas around flat spacetime with
constant temperature. As a result, the multi-horizon black holes in hydrostatic
equilibrium can be in a stable configuration with the aspect of the $q$-kinetic
theory.
