  We discuss the phase transition between non-extremal and extremal
Reissner-Nordstr\"om black holes. This transition is considered as the
  $T \to 0$ limit of the transition between the non-extremal and near-extremal
black holes.
  We show that an evaporating process from non-extremal black hole to extremal
one is possible to occur, but its reverse process is not possible to occur
because of the presence of the maximum temperature.
  Furthermore, it is shown that the Hawking-Page phase transition between small
and large black holes unlikely occurs in the AdS Reissner-Nordstr\"om black
holes.
