Results of a molecular dynamics simulation (MDS) of a Mg²⁺ stabilized form of the well known solid electrolyte Na⁺ beta-alumina (idealized formula: Na_1+xAl_11-xMg_xO₁₇ for x = 0.22) are presented. The simulated crystal is stable over a wide temperature range, while still exhibiting a high degree of mobility for the mobile Na⁺ ion species. Analysis of Na⁺ trajectories is able to identify the conduction mode prevalent at a given temperature. This changes dramatically as the temperature increases; going from an almost conventional hopping motion at low T to highly correlated motion at high T, where a number of ions move over large distances. Remarkably, the transition is found to coincide with a region of reduced overall mobility, with the diffusion constant passing through a local minimum. The mechanisms underlying such phenomena are exposed, and comparisons made with our earlier MDS study of the normal form of Na⁺ beta-alumina, where the charge compensation is achieved through the introduction of an extra oxygen into the conduction plane (the Roth defect). It is shown that significantly different levels of diffusivity can result from different compensation mechanisms.