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We use the spin-rotation-invariant Green's function method as well as thehigh-temperature expansion to discuss the thermodynamic properties of thefrustrated spin-$S$ $J_{1}$-$J_{2}$ Heisenberg magnet on the body-centeredcubic lattice. We consider ferromagnetic nearest-neighbor bonds $J_1 < 0$ andantiferromagnetic next-nearest-neighbor bonds $J_2 \ge 0$ and arbitrary spin$S$. We find that the transition point $J_2^c$ between the ferromagnetic groundstate and the antiferromagnetic one is nearly independent of the spin $S$,i.e., it is very close to the classical transition point $J_2^{c,{\rm clas}}=\frac{2}{3}|J_1|$. At finite temperatures we focus on the parameter regime$J_2<J_2^c$ with a ferromagnetic ground-state. We calculate the Curietemperature $T_{C}(S,J_{2})$ and derive an empirical formula describing theinfluence of the frustration parameter $J_{2}$ and spin $S$ on $T_C$. We findthat the Curie temperature monotonically decreases with increasing frustration$J_2$, where very close to $J_2^{c,{\rm clas}}$ the $T_C(J_2)$-curve exhibits afast decay which is well described by a logarithmic term$1/\textrm{log}(\frac{2}{3}|J_1|-J_{2})$. To characterize the magnetic orderingbelow and above $T_C$, we calculate the spin-spin correlation functions$\langle {\bf S}_{\bf 0} {\bf S}_{\bf R} \rangle$, the spontaneousmagnetization, the uniform static susceptibility $\chi_0$ as well as thecorrelation length $\xi$. Moreover, we discuss the specific heat $C_V$ and thetemperature dependence of the excitation spectrum. As approaching thetransition point $J_2^c$ some unusual features were found, such as negativespin-spin correlations at temperatures above $T_C$ even though the ground stateis ferromagnetic or an increase of the spin stiffness with growing temperature.

Thermodynamics of the frustrated $J_1$-$J_2$ Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin