Temperature significantly affects grandfather clocks with brass pendulums due to the metal's expansion coefficients, which alter the pendulum's length and period. Compensation methods are necessary to maintain accuracy, often requiring innovative solutions that involve materials with different expansion rates. The discussion highlights that brass has a higher coefficient of thermal expansion compared to unalloyed iron, which can impact clock performance. Historical context is provided, mentioning John Harrison's contributions to clock design aimed at solving navigation issues, although his clocks were spring-driven rather than pendulum-based. Understanding these principles is crucial for maintaining the precision of grandfather clocks.