  The Quantum Heisenberg Ferromagnet can be naturally reformulated in terms of
interacting bosons (called spin waves or magnons) as an expansion in the
inverse spin size. We calculate the first order interaction correction to the
free energy, as an upper bound in the limit where the spin size $S \to \infty$
and $\beta S$ is fixed ($\beta$ being the inverse temperature). Our result is
valid in two and three spatial dimensions. We extrapolate our result to compare
with Dyson's low-temperature expansion. While our first-order correction has
the expected temperature dependance, in higher orders of the perturbation
theory cancellations are necessary.
