Self-organized Co nanodots on a Au(111) surface have been surrounded by controlled Au rings that progressively cap the entire dots. The magnetic susceptibility of these dots has been measured in situ as a function of the Au coverage. The blocking temperature increases when the Co bilayer dots are surrounded by the first Au atomic layer and decreases with the subsequent capping. This result cannot be explained by interfacial anisotropy which is generally assumed to be the dominant term in the magnetic anisotropy of nanostructures. Using molecular dynamics simulations, we evidence that the large strain inside the Co clusters is the main driving force for the anisotropy changes during the Au encapsulation.