  We use the rotation-invariant Green's function method (RGM) and the
high-temperature expansion (HTE) to study the thermodynamic properties of the
spin-$S$ Heisenberg ferromagnet on the pyrochlore lattice. We examine the
excitation spectra as well as various thermodynamic quantities, such as the
order parameter (magnetization), the uniform static susceptibility, the
correlation length, the spin-spin correlations, and the specific heat, as well
as the static and dynamic structure factors. We discuss the influence of the
spin quantum number $S$ on the temperature dependence of these quantities. We
compare our results for the pyrochlore ferromagnet with the corresponding ones
for the simple-cubic lattice both having the same coordination number $z=6$. We
find a significant suppression of magnetic ordering for the pyrochlore lattice
due to its geometry with corner-sharing tetrahedra.
