A method of heat-treating a glass substrate where the substrate is thermally treated (such as the formation of films, growth of films, and oxidation) around or above its strain point. After thermally treating the substrate around or above its strain point the glass substrate may be slowly cooled at a rate of 0.01.degree. to 0.5.degree. C./min to achieve maximum shrinkage of the substrate. Following further thermal treatments the substrate may be quickly cooled at a rate of 10.degree. C./min to 300.degree. C./sec to suppress shrinkage of the glass substrate. The substrate can have films such as aluminum nitrate films, silicon oxide films, silicon films, insulating films, semiconductor films, etc. Film formation can occur either before or after thermal treatment of the substrate around or above its strain point and before further thermal treatments.