This paper is focused on overcoming reactor shutdown malfunction and diagnostics due to poor cooling and water drop level within a pressurized water reactor. So the temperature coupling analysis between the heat exchanger (HEX) and the U-tube steam generator (UTSG) is inspected under changes of primary and secondary water temperature. This coupling allows the removal of heat from the UTSG via the HEX. For the UTSG, implicit and explicit solutions for analysis and evaluation of UTSG characteristics are conducted. Scarce explicit models describing the behaviors of the UTSG are available. This analytical framework is proposed to control the water/steam flow within the UTSG of a nuclear power reactor (NPR). Exact performances for temperatures of metal tube temperature and primary water entering and exiting from the tube are derived. There is no one implicit model that can describe the performance characteristics of heat transfer within the UTSG. So a novel simulator declaring the operational behavior of the UTSG in an NPR has been built. This simulator of the UTSG provides exact handling of the UTSG performance characteristics. For the HEX, the exact handling of the HEX including boundary temperature and the primary and secondary interface temperatures are proposed. Three different models are implemented (combinational, steady state, and integral). The possibility of realizing higher steam quality is established through block diagram programming models. Compared to literature results, the built models are validated with high agreement. As a final conclusion, the proposed analyses allow the control of steam generation and flow. The introduced results compensate for the necessity of expensive and complicated controllers within the HEX and UTSG through parameter variation. Accordingly, the performance of the NPR is enhanced.