Modeling and optimization of liquid hydrogen (LH2) pumps require accurate in-cylinder heat transfer correlations. However, the applicability of existing correlations based on gas mediums to LH2 remains to be verified. In this paper, the unsteady heat transfer and fluid flow in a closed LH2 pump cylinder are numerically studied by adopting the gas spring model. The phase shifts and temperature distribution in the closed pump cylinder are investigated. LH2 is less affected by in-cylinder heat transfer and has a more uniform temperature distribution compared to nitrogen gas, while a low-temperature zone appears near the piston face at 120 rpm. Finally, the validity of Lekic's correlation in predicting the heat flux of the LH2 compression process in the closed pump cylinder is verified, and the efficiency decrement versus rotational speed is analyzed based on the correlation. This work would be useful for selecting a proper in-cylinder heat transfer model for predicting the thermodynamic process in reciprocating LH2 pumps.