  A thermodynamic analysis of the black hole solutions coming from the
Einstein-Maxwell-Dilaton theory (EMD) in 4D is done. By consider the canonical
and grand-canonical ensemble, we apply standard method as well as a recent
method known as Geometrothermodynamics (GTD). We are particularly interested in
the characteristics of the so called phantom black hole solutions. We will
analyze the thermodynamics of these solutions, the points of phase transition
and their extremal limit. Also the thermodynamic stability is analyzed. We
obtain a mismatch of the between the results of the GTD method when compared
with the ones obtained by the specific heat, revealing a weakness of the
method, as well as possible limitations of its applicability to very
pathological thermodynamic systems. We also found that normal and phantom
solutions are locally and globally unstable, unless for certain values of the
coupled constant of the EMD action. We also shown that the
anti-Reissner-Nordstrom solution does not posses extremal limit nor phase
transition points, contrary to the Reissner-Nordstrom case.
