Na2O2 is one of the possible discharge products from sodium-air batteries. Here, we report the evolution of the structure of Na2O2 from room temperature to 500 degrees C using variable-temperature neutron and synchrotron X-ray powder diffraction. A phase transition from alpha-Na2O2 to beta-Na2O2 is observed in the neutron diffraction measurements above 400 degrees C, and the crystal structure of beta-Na2O2 is determined from neutron diffraction data at 500 degrees C. alpha-Na2O2 adapts a hexagonal P62m (no. 189) structure, and beta-Na2O2 adapts a tetragonal I4(1)/acd (no. 142) structure. The thermal expansion coefficients of alpha-Na2O2 are a = 2.98(1) x 10(-5) K-1, c = 2.89(1) x 10(-5) K-1, and V = 8.96(1) x 10(-5) K-1 up to 400 degrees C, and a similar to 10% volume expansion occurs during the phase transition from alpha-Na2O2 to alpha-Na2O2 due to the realignment/rotation of O-2(2-) groups. Both phases are electronic insulators according to DFT calculations with band gaps (both indirect) of 1.75 eV (alpha-Na2O2) and 2.56 eV (beta-Na2O2). An impedance analysis from room temperature to 400 degrees C revealed a significant enhancement of the conductivity at T >= 275 degrees C. alpha-Na2O2 shows a higher conductivity (similar to 10 times at T <= 275 degrees C and similar to 3 times at T > 275 degrees C) in O-2 compared to in Ar. We confirmed, by dielectric analysis, that this enhanced conductivity is dominated by ionic conduction.