  We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in
the absence of an external field. Spin wave theory suggests that in a suitable
temperature regime the system behaves effectively as a system of
non-interacting bosons (magnons). We prove this fact at the level of the
specific free energy: if $ S \to \infty $ and the inverse temperature $ \beta
\to 0 $ in such a way that $ \beta S $ stays constant, we rigorously show that
the free energy per unit volume converges to the one suggested by spin wave
theory. The proof is based on the localization of the system in small boxes and
on upper and lower bounds on the local free energy, and it also provides
explicit error bounds on the remainder.
