Spin-wave theory predicts reduced thermal spin-wave excitations due to a magnetic anisotropy. Recent results show that a strong uniaxial in-plane anisotropy in ultrathin Fe/GaAs(001) films indeed stabilizes the ferromagnetic order versus thermal spin excitations [Kipferl , J. Appl. Phys. 97, 10B313 (2005)]. In order to study whether a fourth-order in-plane anisotropy has a similar effect epitaxial Fe70Co30/Au(001) samples with zero magnetocrystalline anisotropy were studied and compared to results for Fe/Au(001). The temperature dependence of the spontaneous magnetization M-S for T < 0.5T(c) can be well described by the Bloch [Z. Phys. 61, 206 (1930)] T-3/2 law in the entire thickness range. However, for each thickness B is reduced in Fe70Co30/Au(001) compared to Fe/Au(001) films despite the reduced anisotropy. This means that the effect of a weak in-plane anisotropy is overcompensated by the enhanced exchange interaction. (C) 2006 American Institute of Physics.