  Measuring with high precision the electrical resistance of highly ordered
natural graphite samples from a Brazil mine, we have identified a transition at
$\sim$350~K with $\sim$40~K transition width. The step-like change in
temperature of the resistance, its magnetic irreversibility and time dependence
after a field change, consistent with trapped flux and flux creep, and the
partial magnetic flux expulsion obtained by magnetization measurements, suggest
the existence of granular superconductivity below 350~K. The zero-field virgin
state can only be reached again after zero field cooling the sample from above
the transition. Paradoxically, the extraordinarily high transition temperature
we found for this and several other graphite samples is the reason why this
transition remained undetected so far. The existence of well ordered
rhombohedral graphite phase in all measured samples has been proved by x-rays
diffraction measurements, suggesting its interfaces with the Bernal phase as a
possible origin for the high-temperature superconductivity, as theoretical
studies predicted. The localization of granular superconductivity at these two
dimensional interfaces prevents the observation of a zero resistance state or
of a full Meissner state.
