We are completing the construction of GIANO, a high resolution near-infrared cryogenic spectrograph for the Telescopio Nazionale Galileo (TNG). Most of the optics are made of aluminium and operate at cryogenic temperature. We evaluated the optical degradation due to mis-matches between the thermal expansion coefficients of the different aluminium parts of the instrument. We performed accurate measurements of the relative thermal expansion coefficients (CTE) of Al-6061 and Al-6082 over the 300–77 K temperatures range. We find that the two alloys have identical thermal expansion coefficient within a maximum (3 σ ) uncertainty of Δ α / α  < 0.28%. Our results show that it is possible to overcome the problem of the alignment of a cryogenic instrument, manufacturing the curved optics, the optics’ holders and the optical bench with different metallic alloys with small CTE mismatch (Al-6061 and Al-6082). This conclusion has also been confirmed by the results of the optical tests with the instrument cooled in the laboratory, showing no significant image quality degradation.