  We report fully relativistic molecular-dynamics simulations that verify the
appearance of thermal equilibrium of a classical gas inside a uniformly
accelerated container. The numerical experiments confirm that the local
momentum distribution in this system is very well approximated by the J\"uttner
function -- originally derived for a flat spacetime -- via the Tolman-Ehrenfest
effect. Moreover, it is shown that when the acceleration or the container size
is large enough, the global momentum distribution can be described by the
so-called modified J\"uttner function, which was initially proposed as an
alternative to the J\"uttner function.
