Mechanical spectroscopy measurements were performed on decagonal quasicrystalline Al-Cu-Fe-Cr coatings of three different thicknesses deposited on a mild steel substrate. The mechanical loss spectra indicate that the internal friction is mostly caused by the quasicrystalline coating and that the contributions of both the steel substrate and the interface are small. The shear modulus measured in torsion increases with temperature, while the Young's modulus measured in flexion behaves normally. This shear modulus anomaly is interpreted as being due to solid friction between cracked segments of the quasicrystalline coating. This phenomenon also explains the broad athermal maximum found to occur in isochronal internal friction measurements. A quantitative model successfully reproducing the observed behaviour has been developed. Finally, the reversible high-temperature exponential background was interpreted as being due to the onset of the brittle-to-ductile transition in the quasicrystalline coating. The measured activation enthalpy is similar to the value that was deduced from compression tests performed at high temperatures on icosahedral Al-Cu-Fe bulk material.