A study is reported of the influences of temperature, circuit resistance, and pulse repetition rate on the ZnO varistor inductive pulse response that is disclosed by voltage overshoot and current undershoot. Exponential time constants are fitted to the voltage overshoot and the current undershoot obtained by using high- and low-impedance pulse supplies, respectively. Nearly identical time constants of a few microseconds are found at room temperature, but the voltage overshoot exhibits a temperature-independent time constant whereas the current undershoot exhibits a shorter time constant at low temperature. However, it is also demonstrated that small increases in circuit resistance can change the shape of the current undershoot and cause a decrease in the calculated time constant. It is concluded that the temperature dependence of the current undershoot is a direct consequence of the temperature dependence of the grain resistivity and that it does not result from a temperature-dependent barrier response. The response to repeated pulses reveals a significant polarization current even when a varistor is in the highly conducting breakdown state. A long-term memory of preceding pulses is associated with this polarization current. The inductive response of a varistor is complicated by the influence of this memory, and a shorter-term memory attributed to the lifetime of electron holes.