This study investigates the impact of thermal gradients (−60/23 °C), arctic temperature (−60 °C), and room temperature (23 °C) on the tensile and flexural properties of woven carbon and Kevlar® fiber-reinforced polymer (FRP) composite materials. A novel custom-built environmental chamber was employed to simulate thermal gradients by exposing opposite sides of the samples to −60 °C and 23 °C simultaneously. The woven carbon and Kevlar® FRP composite materials were manufactured using the vacuum-assisted resin transfer molding (VARTM) process. Then, the samples were conditioned at three distinct temperatures: −60 °C, 23 °C, and a thermal gradient of −60/23 °C. After conditioning, they were subjected to tensile and flexural testing to evaluate their mechanical properties. Finally, a detailed fractographic analysis was performed. The results showed that both carbon and Kevlar® FRP composites experienced an increase in their tensile and flexural properties (stiffness and strength) at lower temperatures (−60/23 °C and −60 °C), accompanied by a decrease in strain at failure when compared to samples tested at 23 °C. The main failure mechanism observed was fiber fracture for all the carbon FRP composite samples across all temperatures. In contrast, Kevlar® samples exhibited a combination of fiber fracture, matrix cracking, and delamination. The samples exposed to thermal gradients experienced brittle failure behavior, like the ones seen in the samples exposed to −60 °C. Their tensile and flexural properties showed intermediate values, falling between the samples conditioned to −60 °C and 23 °C.