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Nano-engineering crystalline materials can be used to tailor their thermal properties. By adding new nanoscale phonon scattering centers and controlling their size, one can effectively decrease the phonon mean free path and hence the thermal conductivity of a fully crystalline material. In this letter, we use the 3$\omega$ method in the temperature range of 100-300 K to experimentally report on the more than threefold reduction of the thermal conductivity of an epitaxially-grown crystalline germanium thin film with embedded polydispersed crystalline \ch{Ge3Mn5} nano-inclusions with diameters ranging from 5 to 25~nm. A detailed analysis of the structure of the thin film coupled with Monte Carlo simulations of phonon transport highlight the role of the nano-inclusions volume fraction in the reduction of the phononic contribution to the thermal conductivity, in particular its temperature dependence, leading to a phonon mean free path that is set by geometrical constraints., Comment: Applied Physics Letters, In press