Phenomena occurring at the interface may significantly modify the properties of magnetic thin films. In this paper, the effect of temperature on the magnetic properties of Co(001)/MgO/Co trilayers is studied. The trilayer structure was modified by partial coverage of Co layers by Au at the Co/MgO interface. It is found that when the quantity of deposited gold is small, formation of islands at the Co/MgO interfaces takes place, which is proved by the topological surface analysis and by the x-ray reflectivity. In the investigated trilayer structure, gradual changes of the easy magnetization axis from the in-plane to the out-of-plane direction are observed during lowering the temperature from 300 to 5 K. The analysis of the ferromagnetic resonance spectra within the multiple-magnetic-layer model system indicates that the surface anisotropy provides a significant contribution to the magnetic anisotropy of complete Co(001)/MgO/Co heterostructure.