  It is known that the linearized Einstein's equation around the pure $AdS$ can
be obtained from the constraint $ \Delta S = \Delta\left< H \right> $, known as
the first law of entanglement, on the boundary $CFT$. The corresponding dual
state in the boundary $CFT$ is the vacuum state around which the linear
perturbation is taken. In this paper we revisit this question, in the context
of $ {AdS}_3/{CFT}_2 $, with the state of the boundary ${CFT}_2$ as a thermal
state. The corresponding dual geometry is a planar BTZ black hole. By
considering the linearized perturbation around this black brane we show that
Einstein's equation follows from the first law of entanglement. The modular
Hamiltonian in a thermal state of the ${CFT}_2$ that we have used has been
recently found in arXiv:1608.01283 [cond-mat.stat-mech].
