Using soft-x-ray magnetic resonant reflectivity measurements, we have studied the layer-resolved temperature dependence of the magnetic structure in a six-monolayer-thick fcc-Fe film grown on Cu(001) by pulsed laser deposition. Temperature-dependent reflectivity curves were fitted on the basis of the Heisenberg Hamiltonian involving only a small number of temperature-independent interlayer and intralayer exchange interaction parameters. Our study supports the model of the formation of the blocks of layers with robust magnetic structure whereas the interblock interactions are relatively weak. The temperature-dependent magnetization profile derived on the basis of the exchange interaction parameters reveals a strong inhomogeneity within the film, which is in agreement with the recent theoretical prediction.