A heat‐conduction equation with linearized radiation cooling boundary conditions is used to calculate the thermal field in a circular window pane heated by thermal radiation (fire) but screened on narrow strips along edges built into the frame. This temperature field is used to calculate a quasi‐static thermal stress field in the pane in the first‐order planar thermal stresses build up at the edges in a narrow strip of a few times the pane thickness. As the radius of the pane grows the edge stresses quickly approach those of the linear strip pane. The round window does not differ much from the strip window in the geometrical region of practical utility in windows. The results also indicate, without explicit calculations, that in rectangular windows the stresses do not concentrate in the corner regions. As the final result of the theoretical work it seems plausible to use simple, general relationships obtained for the strip window as well for all geometries deviating from linear to evaluate approximately the danger of thermal breakage of a pane.