Ab initio calculations for layered Fe/Au(001) superlattices with a set of c
ollinear spin configurations are performed by means of the self-consistent
full-potential linearized augmented-plane-wave method under the generalized
gradient approximation. To study the finite-temperature magnetism of such
superlattices, Monte Carlo (MC) simulations are carried out based on a Heis
enberg model with the exchange parameters extracted from the ab initio tota
l energies and a phenomenological anisotropy constant. It is argued that th
e Curie temperature is rather insensitive to the anisotropy and is essentia
lly determined by the ab initio exchange parameters. Due to the reduced coo
rdination number of the magnetic atoms at interfaces, the Curie temperature
obtained by this ab initio MC scheme decreases as decreasing of Fe layer t
hickness governed essentially by Weiss' law. These results are discussed in
connection with recent experimental and theoretical studies.