The flue gas temperature should be observed frequently and logged because it can provide valuable insights into the efficiency and performance of a combustion system. By monitoring the flue gas temperature, deviations from the expected temperature range can be detected, indicating potential issues such as incomplete combustion, heat exchanger fouling, or fuel supply problems. Logging these observations allows for trend analysis and helps in identifying patterns or abnormalities that may require corrective action to optimize energy efficiency and minimize emissions.