Linear thermal expansivity (α, 1–300 K), heat capacity (Cp, 1–108 K), and electrical resistivity (ρ, 1–300 K) measurements are reported for single grain i-Al61.4Cu25.4Fe13.2 quasicrystals as a function of sample processing. While ρ(T) is sensitive to sample treatment, both Cp and α are relatively insensitive (to a few percent) except at the lowest temperatures (below 4 K), where an inverse correlation between ρ and the electronic Cp coefficient γ appears to exist. Dispersion effects (deviations from Debye-like behavior) in both Cp and the lattice Grüneisen parameter Γ are large and comparable with those for single grain i-Al71Pd21Mn08quasicrystal and its Al72Pd25Mn03 approximant [Phys. Rev. B 65, 184206 (2002)]. Since the 0-K Debye temperature [Θ0=536(2)K] is in reasonable agreement with that from 4-K elastic constants [548(8) K], a previous postulate for AlPdMn that these large dispersion effects are associated with high dispersion lattice modes in off-symmetry directions also appears to apply to i-Al-Cu-Fe. A comparison with other Cp data suggests that the major effects of sample treatment (and composition) are reflected, with a few exceptions, in the values of γ, with remarkably similar lattice contributions.