A mathematical model was developed to study the performance of a counterflow hear exchanger in which both fluid streams are exposed to external heating. It was found that under the external heat transfer condition, the effectiveness of the heat exchanger was drastically reduced. The hot fluid temperature effectiveness increased as the external thermal conductance ratios, R-h and R-c, decreased. For effective operation and to avoid temperature cross, there exist a maximum possible NTU for a given R-h and R-c.