The numerical solution of heat transfer problems may involve substantial execution time, and much of the execution time may be spent in the matrix solver. Iterative solution methods may be more efficient than direct methods for solving a large matrix equation. Although iterative methods have been applied to many fields of engineering simulation, they are not widely used in nuclear reactor simulation. Moreover, the selection of a suitable iterative method depends on the problem. Heat transfer in nuclear reactors is a complex process that includes solid conduction, fluid advection, radiation, and convection between solid and fluid. Thus, the feasibility of matrix iterative solution methods is investigated, and the numerical performance of a selected iterative method is assessed. The preconditioned generalized conjugate residual (PGCR) method is an iterative method used in the integrated systems code (ISC) to simulate heat transfer in a modular high-temperature gas-cooled reactor. The numerical performance of the PGCR method is assessed to determine the computational requirements of the ISC. A steady-state heat transfer problem that includes conduction, convection, advection, and radiation heat transfer is solved in the performance study. The execution time of the PGCR method is obtained in the cases of four matrix sizes and three values of the heat transfer Biot number. The Biot number is varied to examine a complete range of convective heat transfer conditions. The execution time per equation is 0.22 to 0.55 ms on the Cray X-MP and 1.6 to 5.0 ms on the Dec 5000 workstation. These results show that the PGCR method is effective for nuclear reactor heat transfer calculations and provides an efficient and reliable computational performance.