We present the theoretical study of thermodynamical properties of fcc-Cu(001) substrate covered by iron-cobalt monolayer as well as by incomplete iron layer. The effective two-dimensional Heisenberg Hamiltonian is constructed from first principles and properties of exchange interactions are investigated. The Curie temperatures are estimated using the Monte-Carlo (MC) simulations and compared with a simplified approach using the random-phase approximation (RPA) in connection with the virtual-crystal approach (VCA) to treat randomness in exchange integrals. Calculations indicate a weak maximum of the Curie temperature as a function of composition of the iron-cobalt overlayer. While a good quantitative agreement between RPA-VCA and MC was found for iron-cobalt monolayer, the RPA-VCA approach fails quantitatively for low coverage due to the magnetic percolation effect. We also present the study of the effect of alloy disorder on the shape of magnon spectra of random overlayers.