  We analyse in detail the thermodynamics in the canonical and grand canonical
ensembles of a class of non-asymptotically flat black holes of the
Einstein-(anti) Maxwell-(anti) Dilaton theory in 4D with spherical symmetry. We
present the first law of thermodynamics, the thermodynamic analysis of the
system through the geometrothermodynamics methods, Weinhold, Ruppeiner,
Liu-Lu-Luo-Shao and the most common, that made by the specific heat. The
geometric methods show a curvature scalar identically zero, which is
incompatible with the results of the analysis made by the non null specific
heat, which shows that the system is thermodynamically interacting, does not
possess extreme case nor phase transition. We also analyse the local and global
stability of the thermodynamic system, and obtain a local and global stability
for the normal case for 0<\gamma<1 and for other values of \gamma, an unstable
system. The solution where \gamma=0 separates the class of locally and globally
stable solutions from the unstable ones.
