For many practical cases of tempering the temper stresses calculated by ins
tant freezing theories are sufficient and in good agreement with experiment
s. The auhors give a brief summary of the theories by Adams and Williamson,
Bartenev and Indenbom and discuss their numerical implementation. For exam
ple, frozen-in temper stresses are calculated and discussed within the mode
l of a symmetrically cooled, infinite glass plate. Based on the numerical s
olution of the heat conduction equation with a given heat transfer coeffici
ent, especially the influence of the initial temperature of quenching is in
vestigated. Furthermore, a numerical algorithm is presented to calculate th
e temporal evolution of the permanent temper stresses for Indenbom's theory
. Finally, as a practical example, residual stresses are determined in the
surface of a tempered glass-particle composite system.