This paper analyzes the thermal performance of a co-current flow heat exchanger with transient gas outflow. The temperature distributions of the working fluid, heating fluid, and the wall over the length of the heat exchanger are predicted by an integral formulation. The heat transfer rates are determined at various stages of the heat exchanger operation. An integral formulation of the nondimensionalized governing equations is solved numerically, using a time-marching algorithm. The temperature distributions of the working fluid and the wall have an exponential increase from the inlet to the outlet of the heat exchanger. The heating fluid shows an initial decrease and subsequent increase of temperature. A base model for the step change in the mass flow of the working fluid is developed and compared against past data for purposes of validation. In addition, results are presented and discussed for the time-varying performance, during pressure regulated gas outflow from the heat exchanger.