An equation expressing the dependence of the breakdown field strength of polymer dielectrics on ambient temperature has been derived based on the hypothesis of an analogy between the physical phenomenon of breakdown and the mathematical cusp catastrophe. The parameters of this equation were determined, and temperature dependencies of breakdown field strength for polyethylene terephthalate, atactic polypropylene, and polybutadiene were constructed. А high degree of correlation between the published experimental data and the calculated temperature dependencies corresponding to the obtained equation was demonstrated. A good agreement between the characteristic glass transition temperatures and electrical breakdown temperatures for all polymers taken was shown. Our work puts forward a hypothesis suggesting a correlation between the kinetic processes of glass transition and electrical breakdown in these polymers.