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We analyse in detail the thermodynamics in the canonical and grand canonicalensembles of a class of non-asymptotically flat black holes of theEinstein-(anti) Maxwell-(anti) Dilaton theory in 4D with spherical symmetry. Wepresent the first law of thermodynamics, the thermodynamic analysis of thesystem through the geometrothermodynamics methods, Weinhold, Ruppeiner,Liu-Lu-Luo-Shao and the most common, that made by the specific heat. Thegeometric methods show a curvature scalar identically zero, which isincompatible with the results of the analysis made by the non null specificheat, which shows that the system is thermodynamically interacting, does notpossess extreme case nor phase transition. We also analyse the local and globalstability of the thermodynamic system, and obtain a local and global stabilityfor the normal case for 0<\gamma<1 and for other values of \gamma, an unstablesystem. The solution where \gamma=0 separates the class of locally and globallystable solutions from the unstable ones.

Thermodynamics of a class of non-asymptotically flat black holes in Einstein-Maxwell-Dilaton theory