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Temperature dependent internal friction is studied in an Fe₃Ga alloy using a dynamical mechanical analyzer. Apart from several thermally activated relaxation peaks with the Arrhenius parameters (activation energies of 1.05 and 1.85 eV and a pre-factor τ₀ ≈ 10⁻¹⁵s) featuring a Snoek-type and Zener relaxation, respectively, a transient internal friction peak related to a structural transition upon heating is found and analyzed in detail. This peak substantiates an irreversible transition from a D0₃ ordered bcc to an L1₂ ordered fcc lattice, as further confirmed by in situ X-ray diffraction measurements. The transient peak is unambiguously shown to feature a diffusionless phase transition.