The stamp forming process is well suited for high volume production of thermoplastic composite parts. The process can be characterized as highly non-isothermal as it involves local quench-cooling of a molten thermoplastic composite blank where it makes contact with colder tooling. The formability of the thermoplastic composite depends on the viscoelastic material behavior of the matrix material, which is sensitive to temperature and degree of crystallinity. An experimental study was performed to determine the effect of temperature and crystallinity on the storage modulus during cooling for a woven glass fiber polyamide-6 composite material. An increase of two decades in modulus was observed during crystallization. As this will significantly impede the blank formability, the onset of crystallization effectively governs the time available for forming. Besides the experimental work, a numerical model is developed to study the temperature and crystallinity throughout the stamp forming process. A process window can be determined by feeding the model with the experimentally obtained data on crystallization.