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We study the holographic supersymmetric Yang-Mills (SYM) theory, which isliving in a hyperbolic space, in terms of the entanglement entropy. The theorycontains a parameter ($C$) corresponding to the excitation of the SYM theory,and it controls the dynamical properties of the theory. The entanglementtemperature ($T_{ent}$) is obtained by imposing the thermodynamic law for therelative entanglement entropy and the energy density of the excitation. Thistemperature is available at any value of the parameter $C$ even in the regionwhere the Hawking temperature disappears. With this new temperature, thedynamical properties of the excited SYM theory are examined in terms of thethermodynamic law. We could find the signatures of phase transitions of thetheory.

Entanglement temperature for the excitation of SYM theory in (De)confinement phase