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Silica aerogel composite is an excellent thermal insulator for spacecraft under high-temperature and complex air environments. This study intends to evaluate SiC-doped silica aerogel’s thermal insulation performance under large temperature and air pressure differences. In this paper, the hot surface’s temperature response of SiC-doped silica aerogel with different content was studied at significant temperature differences (ΔT) when pressure changes instantaneously. Their thermal insulation performance was evaluated by analyzing the influence of pressure gradients on the unsteady-state heat transfer. When the cold surface’s temperature of the specimen keeps constant at 15 °C and ΔT = 171~912 K, the results demonstrate that the correlative thermal conductivities of silica aerogel with 1% and 5.84% SiC are 0.02223~0.04077 W·m−1·K−1 at P ≈ 10 Pa and 0.03165~0.04665 W·m−1·K−1 at P = 1 atm, respectively. The aerogel composite with 0% SiC showed the best thermal insulation performance at ΔT < 200 K and P ≈ 10 Pa, while the aerogel with 5.84% SiC became the best at ΔT > 700 K and P = 1 atm. In addition, the transient pressure decreases will significantly impair the heat transfer of the gas inside the aerogel, thereby weakening the gaseous thermal conductivity and improving the thermal insulation performance.