Optically excited light emission from CdHgTe nanostructures with 12 to 1100 nm- wide potential wells was studied. The structures were grown by molecular beam epitaxy on GaAs substrates. For structures with size quantization, radiative transitions between the levels of the electrons and light holes were observed. For structures with broad potential wells, optical transitions related to exciton localized at potential fluctuations were recorded. In the latter case, the significant degree of the alloy disorder led to the broadening of photoluminescence (PL) spectra and a considerable Stokes shift that could be traced up to temperature T~230 K. Annealing of the structures improved the ordering and led to the increase in the PL intensity. A remarkable feature of the PL of the structures was rather small decrease of its intensity with temperature increasing from 84 to 300 K. This effect was explained by localization of carriers at potential fluctuations.