Experimental pulse lengthpulse voltage studies of SrTiO3 memristive cells are reported, which reveal nonlinearities in the switching kinetics of more than nine orders of magnitude. The results are interpreted using an electrothermal 2D finite element model. The nonlinearity arises from a temperature increase in a few-nanometer-thick disc-shaped region at the Ti electrode and a corresponding exponential increase in oxygen-vacancy mobility. The model fully reproduces the experimental data and it provides essential design rules for optimizing the cell concept of nanoionic resistive memories. The model is generic in nature: it is applicable to all those oxides which become n-conducting upon chemical reduction and which show significant ion conductivity at elevated temperatures.