An approximate but simple method for the low temperature mechanical testing of polymers is frequently used. It consists of quenching the polymer sample into liquid nitrogen and then installing it on the testing apparatus. The required test temperature is determined by the time where the experiment is started. In this work, the time-temperature patterns of two quenched impact test samples, in high density polyethylene and polyurethane, were first measured and then compared with the values obtained from a graphical method of unsteady-state heat conduction. The agreement between experimental data and calculated values is better than 8% in terms of relative error.