Within a Marnoch heat engine (MHE), a water/glycol mixture transfers heat from the heat source into a set of variable flow heat exchangers and removes heat from adjoining cold heat exchangers. The compressed dry air is used as the working medium in this heat engine. The MHE has four shell and tube heat exchangers, which operate transient and variable flow conditions. A new transient heat transfer model is developed to predict this transient behavior of the heat exchangers for different flow regimes and temperatures. The results from the model are validated against experimental results from an MHE prototype. The heat transfer model shows 85% agreement with measured data from the MHE prototype for the individual heat exchangers. This model can be used for similar shell and tube heat exchangers with straight or U-shaped tubes. The heat transfer model predicts the gas temperature on the shell side, when a step change is imposed on the liquid entering the tubes.