What Heats the Dense Gas in the Galactic Center?
Previous studies using p-H$_2$CO $J=3$--$2$ transitions at 218 GHz suggested widespread high-temperature gas exceeding 60 K and even 100 K in the CMZ, with heating mechanisms possibly related to cosmic rays or turbulent dissipation. However, at temperatures above 100 K, p-H$_2$CO $J=3$--$2$ line emission may lead to significant overestimates of kinetic temperature. This study combines o-H$_2$CO $J=5$--$4$ data from JCMT with p-H$_2$CO $J=3$--$2$ data from APEX to analyze three molecular clouds (The Brick, Sgr A1, and Sgr A2) with high temperatures. We used the non-LTE radiative transfer code RADEX to model spectral lines and constrain physical parameters with multiple line ratios, obtaining more reliable kinetic temperatures. Our results show that the previously reported extreme temperatures ($>100$ K) based on p-H$_2$CO $J=3$--$2$ line ratios are revised downward, with the average kinetic temperatures now constrained to 84--95 K using o-H$_2$CO $J=5$--$4$ line ratios, indicating systematic overestimation in the earlier studies. Further analysis reveals that the relationship between temperature and gas line width aligns more closely with predictions from models incorporating both high cosmic ray ionization rate and turbulent heating, suggesting that these molecular clouds are likely heated by a combination of cosmic-ray and turbulent dissipation mechanisms.