We report on optical studies of exciton localization and recombination kinetics in two single 2.2 nm thick AlxGa1-xN/Alx+0.1Ga0.9-xN quantum well structures (x = 0.55 and 0.6) grown by plasma assisted molecular beam epitaxy on a c-sapphire substrate. Strong localization potential inherent for both the quantum well and barrier regions results in merging of the quantum well and barrier emission spectra into a single broad line centered at 285 nm (x = 0.55) and 275 nm (x = 0.6). Time-resolved photoluminescence measurements revealed surprising temperature stability of the photoluminescence decay time constant (approximate to 400 ps) relevant to the recombination of the quantum well localized excitons. This observation implies nearly constant quantum efficiency of the quantum well emission in the whole range from 4.6 to 300 K.