  We use holographic techniques to calculate the first thermal correction to
the entanglement entropy of a cap-like region of a CFT defined on a sphere,
successfully reproducing the field theory result. Since this is an order-one
correction to the entropy in the large-$N$ expansion, quantum corrections to
the holographic entanglement entropy formula are essential. The bulk
calculation is made tractable using the same technical machinery recently used
to derive the linearized Einstein equations in the bulk from the first law of
entanglement entropy in the CFT.
