Nuclear thermal propulsion systems are currently being investigated for future manned missions to Mars. Many recent works analyzing these systems have relied on Monte Carlo neutronics codes such as Serpent and MCNP to accurately calculate fission source distributions. However, these methods can be computationally expensive, especially if multiple iterations are required, such as procedures to account for temperature feedback. Fission matrix-based methods can significantly reduce computational expense in situations that require a series of neutronics calculations, while maintaining near-Monte Carlo levels of accuracy. These methods rely on Monte Carlo techniques to pre-calculate reference data, which is used in subsequent calculations. The present work explores the application of fission matrix methods to nuclear thermal propulsion systems in order to account for fuel temperature feedback and control drum movement. For the cases considered, multiplication factors calculated using fission matrix methods agree with those calculated using Serpent within ±45 pcm. RMS normalized fission source errors are less than 1%, and maximum normalized fission source errors are less than 4%. After calculation of the initial fission matrix database, individual fission matrix calculations take 208 CPU∙seconds to complete.