Temperature dependent photoluminescence (PL) of MgZnO epitaxial layers with high Mg content were studied to understand the effect of carrier localization on the PL dynamics, including the PL dependence on excitation power density and temperature. A double blueshift of the PL peak position with increase of measurement temperature was discovered. The blueshift took place at low as well as high temperature and could be attributed to the effect of carrier localization. It has been deduced that the randomly distributed carrier localization centers in the MgZnO films create two energy separated Gaussian-shape density-of-states tails in the vicinity of the fundamental band gap edge. Filling of these tail states by the thermally activated carriers with increase of temperature causes the temperature-induced double blueshift of the PL peak position. By analyzing the temperature dependent PL spectra, two parameters, σ and γ were extracted, which characterize the average energy depth distribution of the localizing potential field fluctuations. The value of these parameters were found to depend on the Mg content and crystalline structure of the MgZnO epitaxial layers.