We have studied the dependence of the low electric field conductivity of the charge density wave (CDW) system o-TaS(3) on the temperature and applied electric field history. Without the application of high electric fields, the conductivity is higher on cooling than on heating in a wide temperature range below the CDW transition. With the application of increasing field at a given temperature the conductivity evolves towards a stable, history-independent value situated between the cooling and heating values. The evolution is gradual but most pronounced around the threshold field for nonlinear conductivity. The relative change of conductivity after the application of high field is asymmetric in respect of the temperature history. We discuss the results within the model of quantized changes of the CDW wavelength induced by the variation of the temperature and the electric field.