Carbon fibers (CFs) are gaining increasing importance in lightweight composites, but their high price and reliance on fossil-based raw materials stress the need for renewable and cost-efficient alternatives. Kraft lignin and cellulose are renewable macromolecules available in high quantities, making them interesting candidates for CF production. Dry-jet wet spun precursor fibers (PFs) from a 70/30 w/w blend of softwood kraft lignin (SKL) and fully bleached softwood kraft pulp (KP) were converted into CFs under fixation. The focus was to investigate the effect of carbonization temperature and time on the CF structure and properties. Reducing the carbonization time from 708 to 24 min had no significant impact on the tensile properties. Increasing the carbonization temperature from 600 to 800 °C resulted in a large increase in the carbon content and tensile properties, suggesting that this is a critical region during carbonization of SKL:KP PFs. The highest Young's modulus (77 GPa) was obtained after carbonization at 1600 °C, explained by the gradual transition from amorphous to nanocrystalline graphite observed by Raman spectroscopy. On the other hand, the highest tensile strength (1050 MPa) was achieved at 1000 °C, a decrease being observed thereafter, which may be explained by an increase in radial heterogeneity.