In the past, precision optical glass lenses were produced through multiple processes such as grinding and polishing, but mass production of aspheric lenses requiring high accuracy and having complex profile was rather difficult. In such a background, the high-precision optical GMP processes were developed with an eye to mass production of precision optical glass parts by molding press. Generally because the forming stage in a GMP process is operated at high temperature above $570^{circ}C$, thermal stresses and deformations are generated in the aspheric glass lens mold that is used in GMP process. Thermal stresses and deformations have negative influences on the quality of a glass lens and mold, especially the height of the deformed glass lens will be different from the height of designed glass lens. To prevent the problems of a glass lens mold and the glass lens, it is very important that the thermal stresses and deformations of a glass lens mold at high forming temperature are considered at the glass molds design step. In this study as a fundamental study to develop the molds used in an aspheric glass lens fabrication, a heat transfer and a thermal stress analysis were carried out for the case of one cavity glass lens mold used in progressive GMP process. Finally using analysis results, it was predicted the height of thermally deformed guide ring and calculated the height of the guide ring to be modified, $64.5{mu}m$. This result was referred to design the glass lens molds for GMP process in production field.