  Assuming only statistical mechanics and general relativity, we calculate the
maximal temperature of gas of particles placed in AdS space-time. If two
particles with a given center of mass energy come close enough, according to
classical gravity they will form a black hole. We focus only on the black holes
with Hawking temperature lower than the environment, because they do not
disappear. The number density of such black holes grows with the temperature in
the system. At a certain finite temperature, the thermodynamical system will be
dominated by black holes. This critical temperature is lower than the Planck
temperature for the values of the AdS vacuum energy density below the Planck
density. This result might be interesting from the AdS/CFT correspondence point
of view, since it is different from the Hawking-Page phase transition, and it
is not immediately clear what effect dynamically limits the maximal temperature
of the thermal state on the CFT side of the correspondence.
