This paper studies the performance of the primary and secondary flow paths of the Heat Exchangers (HEXs) in the Nuclear Power Plants (NPP). Explicit solutions for the wall temperature, primary and secondary wall temperatures of the HEX are presented. Therefore, closed form expressions for wall temperature, primary and secondary wall temperature are proposed. Moreover, performance analysis of HEX is investigated. Curves for the HEX wall temperature are introduced with special emphasis on the initial wall temperature. The various effects of pipe wall heat capacities, perimeter, fluid Heat Transfer (HT) coefficient and wall HT coefficient on the HEX are evaluated. The obtained results confirm that the surface contact between the two fluid passes reduces the temperature to some extent at 5 seconds. Furthermore, it is limited to the pipe length and contact time. As a final point of observation, the distributed temperature through the HEX structure increases with the decrease of perimeter. Since, the wall area decreases with the decrease of perimeter. The proposed work allows more control of the HT process within the HEX. Consequently, the performance of NPPs can be improved.