In the case of reversible heat exchange which the cooler body rises in temperature from T1 to T2, it requires that the temperature difference between the system and the heat source must be infinitesimal in every step. Usually the model is like that: Give a heat reservoir of temperature slightly higher than T1, make a small amount of heat transfer, than the temperature of cold body rise a little bit. Then use another hotter reservoir and transfer another infinitesimal amount of heat, repeat the steps until the body is T2. The problem is: In every step the entropy decrease of hotter reservoir is smaller than the entropy increase of the cooler body. There is a net increase in entropy of the system. Although the increase is close to zero, we have done infinite number of step in order to increase the temperature to T2. How can we ensure the overall increase in entropy is zero so that it is a reversible process?