An upper bound of the relative entanglement entropy of thermal states at an inverse temperature \(\beta\)  of linear, massive Klein-Gordon and Dirac quantum field theories across two regions, separated by a nonzero distance \(d\) in a Cauchy hypersurface of an ultrastatic (spin-)spacetime has been computed. This entanglement measure is bounded by a negative constant times \(\mathrm{ln}|\tanh(\pi d/2\beta)|\) which signifies power law decay for asymptotic \(d\) where the exponent depends on \(\beta < \infty\).