The plasma sheath is produced by high-temperature heating during the reentry of a hypersonic vehicle to the Earth atmosphere. Temperature around the vehicle rises rapidly because of severe friction with air. The vehicle temperature behind friction is high enough to excite various real gas effects including chemical reactions of air, which contains ablation particles of vehicle, free electrons, and ions. The plasma sheath greatly affects the transmission of electromagnetic waves and has very strong interference on the communication signals, which results in interrupt between the target and the ground station, namely, blackout. The electron density of plasma sheath surrounding the aircraft is inhomogeneous and varies with time. Temperature and pressure will also change at different altitudes. Therefore, it is meaningful to investigate the propagation characteristics of electromagnetic waves in temporally and spatially inhomogeneous plasma sheath. The temporally and spatially inhomogeneous plasma sheath model is introduced and the electron density data of the National Aeronautics and Space Administration (NASA) reentry vehicle is employed. The relationships among temperature, pressure, and collision frequency are obtained with the empirical formula of collision frequency. Then, the reflection coefficient and transmission coefficient of time-varying single layer plasma are calculated with the shift operator finite-difference time-domain (SO-FDTD) method. These results are compared to verify the correctness of the proposed method. Finally, the LTJEC-FDTD method is used to calculate the reflection coefficient, transmission coefficient and absorptivity at different relaxation time, temperature, and pressure in the terahertz (THz) band. The results show that the higher temperature and pressure will enable the electromagnetic wave to penetrate the plasma sheath at high relaxation time of electron density. If the incident wave frequency is lower than the cut-off frequency of plasma, the reflection of electromagnetic wave will be more obvious. However, when the incident wave frequency is in the THz band, the effects of temperature and pressure on the propagation of electromagnetic wave are obviously weakened. The absorption of electromagnetic wave by plasma will be more obvious when the relaxation time, temperature, and pressure decrease. If the relaxation time of electron density is shorter than or equal to the period of THz wave, more energy of electromagnetic wave will be absorbed by the plasma sheath. Contrarily, if the relaxation time of electron density is much longer than the period of THz wave, the absorption of electromagnetic energy will decrease. This study gives some insight into the temporally and spatially inhomogeneous plasma sheath, and provides a theoretical basis for solving the blackout problem.