  We adopt the Dirac model for quasiparticles in graphene and calculate the
finite temperature Casimir interaction between a suspended graphene layer and a
parallel conducting surface. We find that at high temperature the Casimir
interaction in such system is just one half of that for two ideal conductors
separated by the same distance. In this limit single graphene layer behaves
exactly as a Drude metal. In particular, the contribution of the TE mode is
suppressed, while one of the TM mode saturates the ideal metal value. Behaviour
of the Casimir interaction for intermediate temperatures and separations
accessible for an experiment is studied in some detail. We also find an
interesting interplay between two fundamental constants of graphene physics:
the fine structure constant and the Fermi velocity.
