The ferromagnetic-phase transition in the invar alloy system Fe₆₅Ni₃₅ was investigated. Neutron depolarization data along with SANS data indicate a broadening of the phase transition. To interpret the data, we introduce a position-dependent Curie temperature T_C, which fluctuates around an average value 〈T_C〉. The local T_C-variations are described by the standard deviation of the transition temperature, ΔT_C, and by the characteristic correlation length R₀. The deduced parameters for Fe₆₅Ni₃₅ are: 〈T_C〉 = 485 ± 0.5K, ΔT_C = 12.5 ± 0.2K and R₀ ≈ 6 × 10³ Å. The magnetic transition can be described by a percolative scenario, as the criterium R₀/a ≫ (ΔT_C/〈T_C〉)^-2/3 is fulfilled, where a is the lattice constant.