One of the challenging tasks related to lithium-ion batteries (LIBs) remains a comprehensive approach for battery behaviour modelling. An approach is presented that enables modelling the voltage-capacity response of LIBs that are subjected to variable temperature and current load histories. A detailed presentation of the developed macro-scale phenomenological model embedding the mechanistic properties of the Prandtl type hysteresis operator and the concept of the force-voltage analogy is made. The necessary input data preparation for the model calibration is also presented. Accuracy of the model is confirmed with experimental observations for both nested current load history at two different temperatures and for arbitrary current load history. The same measured data is used to calibrate and to simulate response of the first order Thevenin equivalent circuit topology in order to amply compare the obtained results.