  In this paper, we study entanglement islands and the Page curve in the
eternal four-dimensional Schwarzschild black hole surrounded by finite
temperature conformal matter. By finite temperature conformal matter we mean
the matter described by the thermal density matrix, rather than the usually
considered matter above the Fock vacuum. We take the matter and the black hole
at different temperatures and calculate the entanglement entropy for such a
setup using the s-wave approximation. As a result, we obtain that at late times
the island prescription leads to the exponential growth of the entanglement
entropy of conformal matter in thermal vacuum.
