We have designed a novel temperature-responsive dialysis system consisting of mixed electrolyte solutions and an ionic gel whose charge density changes in response to temperature changes. The system can modulate the time-concentration profile of just bivalent ions in arbitrary forms by changing the transport modes of the ions in response to the temperature, as long as the system has a sufficient concentration difference of the driving electrolyte for the modulation. The simulation in a model system consisting of mixed KCl and CaCl2 solutions and the ionic gel shows that the system modulates the time-concentration profile of Ca2+ ions as a sawtooth waveform, and also keeps the concentration a prearranged value for a certain time period by controlling the transport modes of just Ca2+ ions in two ways: downhill (transport along their own concentration gradient in a system) and uphill (transport against their own concentration gradient), in response to temperature changes. The simulations agree quantitatively with the experiments using a temperature-responsive ionic gel prepared in the previous paper.