  We consider the pyrochlore-lattice quantum Heisenberg ferromagnet and discuss
the properties of this spin model at arbitrary temperatures. To this end, we
use the Green's function technique within the random-phase (or Tyablikov)
approximation as well as the linear spin-wave theory and quantum Monte Carlo
simulations. We compare our results to the ones obtained recently by other
methods to corroborate our findings. Finally, we contrast our results with the
ones for the simple-cubic-lattice case: both lattices are identical at the
mean-field level. We demonstrate that thermal fluctuations are more efficient
in the pyrochlore case (finite-temperature frustration effects). Our results
may be of use for interpreting experimental data for ferromagnetic pyrochlore
materials.
