Infrared optical studies were carried out in a group of cubic InN samples grown by gas source molecular beam epitaxy on MgO (001) substrates. Room temperature (RT) reflectance and low-temperature (LT) transmittance measurements were performed by using fast Fourier transform infrared spectrometry. Reflectance fittings allowed to establish that β-InN films have large free-carrier concentrations present (>1019 cm-3), a result that is corroborated by Hall effect measurements. Each sample explored exhibited a different optical absorption edge. The Varshni parameters that describe adequately the optical absorption edge responses with temperature are obtained for the set of samples studied. The observed temperatures changes, from LT to RT, are the lowest reported for III-V semiconductor binary compounds. The temperature coefficient of the conduction band depends on the strength of the electron–phonon interaction (e-ph-i), as well as on the thermal expansion. It has been predicted that cubic InN has one of the smallest e-ph-i of all III-V compounds, which is corroborated by these results. The variation in values of absorption edges is clearly consistent with the Burstein–Moss and band renormalization effects, produced by high free electron concentrations. It is shown that the conduction band in β-InN, analogous to wurtzite InN, follows a nonparabolic behavior.