The main bottleneck of using composites for cryogenic storage of clean hydrogen fuel is the permeation of gas molecules. In this work, the permeation of hydrogen gas through thermally cycled thermoplastic composite laminates with two different stacking sequence is investigated. The experimental study is based on a methodology of cryogenically cycling the composite specimen and measuring the permeability in a dedicated hydrogen permeation setup. An optical microscope and X-ray computed tomography scanner are employed to investigate the existence of cracks. The results reveal that thermal cycling does not have a profound influence on permeability, while the stacking sequence has a considerable effect. Laminates with dispersed 0° layers resulted in lower permeation values compared to the laminate with grouped 0° layers at the laminate’s core. The imaging techniques did not reveal any observable crack which supports the hypothesis that permeation is mostly driven by bulk diffusion in the polymer.