The transient thermal conditions in problems involving flowing fluid systems in contact with heat capacitors are becoming increasingly important with the advent of modern control techniques. The temperature controlability of a flowing fluid system is a direct function of the transient thermal response of the fluid to a specific temperature input function. In a previous paper, the author presented an analysis which considered the transient fluid temperatures in a system consisting of a compressible fluid flowing through a duct or in a heat exchanger. The case of a compressible fluid, with an exponential or step-function fluid temperature input, flowing through an insulated tube or pipe was analyzed in detail and examples were presented. The treatment of the transient conditions for a compressible fluid flowing through a heat exchanger was partially analyzed and the method of solution was demonstrated. The present paper consists of an extension of this work in which the transient conditions due to thermal lags in flowing incompressible fluid systems are analyzed. Both the case of an incompressible fluid, with a step-function temperature input, flowing through a circular tube or pipe and the case of an incompressible fluid flowing in a simple heat exchanger are examined in detail. An example which demonstrates the transient condition at the exit of a simple (condensing-steam/water) heat exchanger is presented also.