Thermospheric temperature and density recovery during the 5 April 2010 geomagnetic storm has been investigated in this study. Neutral density recovery as revealed by Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM) simulations was slower than observations from GOCE, CHAMP, and GRACE satellites, suggesting that the cooling processes may not be fully represented in the model. The NO radiative cooling rate in TIEGCM was also compared with TIMED/SABER measurements along satellite orbits during this storm period. It was found that the model overestimated the NO cooling rate at low latitudes and underestimated it at high latitudes. The effects of particle precipitation on NO number density and NO cooling rate at high latitudes were examined in detail. Model experiments showed that while NO number density and NO cooling rate do change with different specifications of the characteristic energy of auroral precipitating electrons, neutral temperature and density recovery remain more or less the same. The reaction rates of key NO chemistry were tested as well, and the NO number density between 110 and 150 km was found to be very sensitive to the reaction rate of N(²D) + O₂ → NO + O. A temperature-dependent reaction rate for this reaction proposed by Duff et al. (2003) brought the TIEGCM NO cooling rate at high latitudes closer to the SABER observations. With the temperature-dependent reaction rate, the neutral density recovery time became quite close to the observations in the high-latitude Southern Hemisphere. But model-data discrepancies still exist at low latitudes and in the Northern Hemisphere, which calls for further investigation.