We employ molecular beam epitaxy to stabilize Ba2IrO4 thin films and utilize in situ angle-resolved photoemission spectroscopy to investigate the evolution of its electronic structure through the Néel temperature TN. Our measurements indicate that dispersions of the relativistic Jeff=1/2 and 3/2 bands exhibit an unusual dichotomy in their behavior through the Néel transition. Although the charge gap survives into the paramagnetic state, only the Jeff=1/2 state exhibits a strong temperature dependence and its gap softens with increasing temperature approaching TN, while the nearly fully occupied Jeff=3/2 state which remains nearby in energy exhibits negligible changes with temperature. © 2014 American Physical Society.