Effective exchange interactions in bulk ferromagnets as well as in magnetic overlayers on Cu(001) covered by a Cu-cap layer of varying thickness were determined from first principles by mapping of corresponding total energies onto the effective Heisenberg model in the framework of the adiabatic approximation and magnetic force theorem. The effective Heisenberg model is then used to determine spin-wave stiffness constants and Curie temperatures evaluated in the framework of the random-phase approximation. Calculations are in a fair agreement with experimental data for bulk ferromagnets and reproduce an oscillatory Curie temperature of magnetic overlayers as a function of Cu-cap thickness in a qualitative agreement with recent experiments.