A thermal stress field induced by a line heat source often causes crack extension. Taking advantage of this phenomenon, some glassy materials can be cleaved without leaving any microcracks on the cleaved surface. In the present paper, the time dependent stress intensity factor of a line crack pre-introduced from the end of a thin plate has been obtained when a thin plate is heated by a continual line heat source on a crack. The stress intensity factor is affected by the width of the strip and the ligament length but is almost independent from the crack length. The present analysis agrees well with the experimental results using glass plates. The section of the glass cleaved by a line heat source was extremely smooth. The surface roughness was within 0.02μm at Ra.