The Fe-projected phonon density of states (PDOS) of monolayer-thick films of self-assembled, size-selected, isolated ⁵⁷Fe_1−xPt_x alloy nanoclusters (NCs) (height:  ∼ 2 nm, diameter:  ∼ 8 nm) supported on flat SiO₂/Si(111) substrates has been measured by nuclear resonant inelastic x-ray scattering. The samples were characterized by atomic force microscopy (AFM), transmission electron microscopy, and x-ray photoelectron spectroscopy (XPS). Surface segregation of Pt and PtSi formation at the NC surface due to the sample-preparation process is inferred from the XPS data. As compared to the bulk, pronounced modifications of the PDOS beyond the bulk cut-off energy are observed in bcc ⁵⁷Fe_0.8Pt_0.2 (core)/PtSi(shell) NCs. By contrast, the PDOS of fcc ⁵⁷Fe_0.75Pt_0.25 (core)/PtSi(shell) NCs retains features of bulk ordered Fe₃Pt Invar alloys (presumably due to a thicker PtSi shell), in particular, the transverse-acoustic [110] TA₁ mode near 9 meV. Apparently, this mode is not affected by size effects. The existence of the [110] TA₁ phonon mode is a prerequisite for the persistence of Invar-related effects in Fe₃Pt NCs. Important thermodynamic properties of the NCs are derived, such as the vibrational entropy per atom.