This study provides a comprehensive analysis of the moderator temperature coefficient (MTC) of a conventional graphite-moderated High-Temperature Gas-cooled Reactor (HTGR) loaded with a burnable absorber based on boron carbide. Emphasizing the significant neutron spectrum differences, the investigation explores how the changes influence the reaction rates (RRs), particularly at the end of life (EOL), considering the depleted fuel composition. The study concludes with an isotopic RR analysis, identifying the key contributors to the positive MTC at EOL for HTGRs. Assumptions are validated through direct manual computation of the MTC. This single-fuel-assembly-level study highlights the impact of spectrum evolution during depletion, revealing a shift from a strongly negative MTC at the beginning of life (BOL) to a slightly positive MTC at EOL. Graphite capture emerges as the major contributor to the MTC at both BOL and EOL, with initially beneficial and subsequently adverse effects. At EOL, 239Pu and 241Pu contribute to the positive MTC values as well, in conjunction with graphite capture as the primary factor. These findings offer valuable insights for higher power density HTGRs. All calculations were performed utilizing the Continuous Monte Carlo Code Serpent 2 and the ENDF/B VII.1 nuclear library.