  We compute the entanglement temperature using the first law-like of
thermodynamics, $\Delta E=T_{ent} \Delta S_{EE}$, up to Gauss-Bonnet term in
the Jacobson-Myers entropy functional in any arbitrary spacetime dimension. The
computation is done when the entangling region is the geometry of a slab. We
also show that such a Gauss-Bonnet term, which becomes a total derivative, when
the co-dimension two hypersurface is four dimensional, does not contribute to
the finite term in the entanglement entropy. We observe that the Weyl-squared
term does not contribute to the entanglement entropy. It is important to note
that the calculations are performed when the entangling region is very small
and the energy is calculated using the normal Hamiltonian.
