During the operation of a Nuclear Steam Supply System (NSSS), the possibility exists for certain thermal transients to occur in the Reactor Coolant System (RCS). These transients exhibit some amount of periodicity in terms of temperature versus time. The current method of solving for temperature or thermal-mechanical stress states in the nuclear pressure vessel industry is by solving the governing equations in the time domain. For some analytical situations, significant computational savings could be realized by solving the thermal transient problem in the frequency domain. That is, the time, memory, and disk space required to solve the analysis is much less in the frequency domain than in the time domain. Two frequency domain methods are discussed in this paper. First, a Laplace-based model order reduction approach is applied to a reactor vessel component subjected to a representative thermal transient. Second, the feasibility of a Fourier-based spectral approach is discussed. For transient thermal analysis, it is shown that by employing model order reduction, significant computational savings can be realized with insignificant compromise in the accuracy of results.