First of all, this article aimed to evidence the role of a modified printer developed for continuous carbon fibre reinforced PolyAmide (cCF/PA6-I) together with the use of a fully open slicing step on the printing quality and the longitudinal/transverse tensile and in-plane shear properties. A comprehensive assessment of the microstructure and properties with a similar material (cCF/PA6-I), but produced with a commercial printer (i.e., Markforged® MarkTwo) has been achieved. Our customised printer and the open slicer used have made possible to better control the print conditions (i.e., layer height and distance between filaments), to reduce the porosity from more than 10% to about 2% and improve the mechanical properties. Moreover, the understanding of the behaviour of these 3D printed composites with wide-ranging external temperatures is mandatory for future use in a severe environment and/or development of new thermally active 4D printed composites. The 3D printed cCF/PA6-I composites have been then thermomechanically characterised along different printing directions (0, 90 and ± 45°) from −55 to +100 °C. Unlike the longitudinal properties that hardly change with temperature, the transverse and in-plane shear stiffness and strength of these 3D printed composites were particularly sensitive to temperature variations, with decreases of 25–30% and 30–55%, respectively. This was due to the high sensitivity of the polymer matrix, the fibre/matrix and interfilament interfaces when the composites were loaded along those directions, because damages induced by internal thermal stresses. Fractography has also been carried out to reveal damage mechanisms.