  We present a theory of the finite temperature thermo-electric response
functions of graphene, in the hydrodynamic regime induced by electron-electron
collisions. In moderate magnetic fields, the Dirac particles undergo a
collective cyclotron motion with a temperature-dependent relativistic cyclotron
frequency proportional to the net charge density of the Dirac plasma. In
contrast to the undamped cyclotron pole in Galilean-invariant systems (Kohn's
theorem), here there is a finite damping induced by collisions between the
counter-propagating particles and holes. This cyclotron motion shows up as a
damped pole in the frequency dependent conductivities, and should be readily
detectable in microwave measurements at room temperature. We also discuss the
large Nernst effect to be expected in graphene.
