We report on the thermal evolution of the photoluminescence (PL) from high In-content InN/In0.9Ga0.1N multiple-quantum wells (MQWs) synthesized by plasma-assisted molecular-beam epitaxy on GaN-on-sapphire templates. The structural quality and the well/barrier thickness uniformity in the MQW structure are assessed by X-ray diffraction and transmission electron microscopy measurements. PL results are compared with the luminescence from a 1-µm-thick InN reference sample. In both cases, the dominant low-temperature (5 K) PL emission peaks at ∼0.73 eV with a full width at half maximum of ∼86 meV. The InN layer displays an S-shape evolution of the emission peak energy with temperature, explained in terms of carrier localization. A carrier localization energy of ∼12 meV is estimated for the InN layer, in good agreement with the expected carrier concentration. In the case of the MQW structure, an enhancement of the carrier localization associated to the piezoelectric field results in an improved thermal stability of the PL intensity, reaching an internal quantum efficiency of ∼16%.