In this study, cryogenic (77 K) to ambient (293 K) thermal shocks are induced to investigate the material behavior and failure characteristic of a random glass-mat-reinforced thermoplastic (GMT). The GMT has numerous advantages such as robust thermal conductivity, good mechanical strength, and good impact resistance. Hence, the GMT serves as an insulation material in liquefied natural gas (LNG) carrier-cargo containment systems (CCSs). In this study, 50, 100, 200, 400, and 800 cryogenic thermal cyclic shocks (77 K to 293 K) were applied to the fabricated GMT samples. The time for each cycle was 40 min, and it took up to approximately four months to completely apply the thermal cyclic shock to the specimens. The elongation, tensile strength, and elastic modulus of the testing samples obtained from the stress–strain relationship and morphologies were investigated in terms of the number of thermal cyclic shocks and strain rate. Finally, explicit formulae were proposed considering the parameters such as material properties and number of cryogenic thermal cycles to predict the material capabilities under arbitrary loading rates and cryogenic thermal cycles. It was confirmed that the degradation and defects increased with an increase in the number of cryogenic thermal cycles.