Ultrathin glass is a promising substrate material for web processing (also called roll-to-roll processing) of flexible electronics, but is highly susceptible to breaking and cracking due to the almost inevitable presence of substrate-edge defects. Recently, a novel technique for removing the micro cracks on the edges of ultrathin glass substrates was devised at ITRI. It amounts to shining a CO2 laser on one edge of a substrate, which induces spontaneous peeling of a thin layer containing preexisting cracks on the edge from the substrate, resulting in an essentially crack-free new substrate edge. Exploiting the thinness of ultrathin glass substrates, here we propose a simplified two-dimensional thermal model for the laser peeling process, and obtain an analytic expression for the transient temperature variation in a substrate being peeled. This enables us to locate the "thermally affected zone" in the substrate, which turns out to be impressively similar in size and shape to the substrate-edge peels observed in experiments. Moreover, a quantitative criterion for the minimum cooling rate required for the progression of the peeling process is obtained. The results here thus provide useful insights into the laser peeling mechanism, and can be used to expedite the optimization of process parameters. Some preliminary purely numerical results using a finite element method (FEM) based software also are briefly discussed here.