  Temperature in a simple thermodynamical system is not limited from above. It
is also widely believed that it does not make sense talking about temperatures
higher than the Planck temperature in the absence of the full theory of quantum
gravity. Here, we demonstrate that there exist a maximal achievable temperature
in a system where particles obey the laws of quantum mechanics and classical
gravity before we reach the realm of quantum gravity. Namely, if two particles
with a given center of mass energy come at the distance shorter than the
Schwarzschild diameter apart, according to classical gravity they will form a
black hole. It is possible to calculate that a simple thermodynamical system
will be dominated by black holes at a critical temperature which is about three
times lower than the Planck temperature. That represents the maximal achievable
temperature in a simple thermodynamical system.
