The tensile properties of thermoplastic composites based on hybrid yarn structures consisting of recycled carbon fibre (rCF) and thermoplastic fibres (rCF content of the hybrid yarn approx. 50–60% by weight) have been reported previously. To date, no report has been found on the tensile properties of thermoset composites based on yarns with high rCF content (>90% by weight). The reasons for this are the complex mechanisms involved in processing pure rCF due to the low shear strength, smooth fibre surface, small fibre diameter and high brittleness of rCF. Yarns made of rCF (≥90% weight) for thermoset composites have been developed in a fundamental research project at the ITM. This paper reports on the tensile properties of unidirectional composites based on yarns composed of staple rCF (>90%) and low melting co-polyamide fibres produced by varying spinning parameters. Furthermore, in order to increase the infiltration of the epoxy matrix during the composite manufacturing process, the yarns are thermally treated at 180°C prior to infiltration and its effect on the tensile properties of the composites is analysed. The results show that the thermal treatment of the yarn prior to infiltration with the matrix, compared to the yarn without prior thermal treatment, helps to achieve better impregnation and therefore better tensile strength of the composites compared to the yarn without prior thermal treatment. A Youngs’ modulus and tensile strength of 86 ± 11 GPa and 1181 ± 71 MPa respectively are achieved in thermoset composites based on the developed yarns.