A thermal edge finishing process includes preheating at least one cut edge of a glass sheet, laser finishing the edge to a single full continuous radius from a position orthogonal to the edge and in-plane with the glass sheet while continuing to heat the glass, and localized annealing of the edge to reduce residual stress from the laser/thermal treatment of the edge. By the present process, edge stress is reduced considerably, such as to less than 3000 psi, and more preferably to less than 2500 psi, and to as low as 1000 psi in the first 1 mm along the treated edge.