  We unveil a transition from single peaked to bimodal velocity distribution in
a relativistic fluid under increasing temperature, in contrast with a
non-relativistic gas, where only a monotonic broadening of the bell-shaped
distribution is observed. Such transition results from the interplay between
the raise in thermal energy and the constraint of maximum velocity imposed by
the speed of light. We study the Bose-Einstein, the Fermi-Dirac, and the
Maxwell-J\"uttner distributions, all exhibiting the same qualitative behavior.
We characterize the nature of the transition in the framework of critical
phenomena and show that it is either continuous or discontinuous, depending on
the group velocity. We analyze the transition in one, two, and three
dimensions, with special emphasis on two-dimensions, for which a possible
experiment in graphene, based on the measurement of the Johnson-Nyquist noise,
is proposed.
